© Nuccio DiNuzzo/Chicago Tribune Joakim Noah runs off the court after his team's 103-86 win over the Pacers at the United Center.

The Chicago Bulls just had one of the most active offseasons in the NBA, overhauling much of their roster in an attempt to get back to the playoffs. They added DeMar DeRozan, Lonzo Ball, Alex Caruso and Tony Bradley in free agency and acquired Derrick Jones Jr. in a trade — all of whom should factor into the rotation.

Yet after all that activity and with about four weeks until training camp starts, there’s a chance the Bulls are not done tinkering.

They have 13 players signed to guaranteed contracts and one two-way player (Devon Dotson), which gives them room for at least one more addition before the season with holes to fill in the frontcourt. Teams need at least 14 players by the end of training camp with a maximum of 15 (not including two-way contracts).

© Chris Sweda/Chicago Tribune Joakim Noah puts on his warmup after being pulled from the game.

Here are the players currently under contract with the Bulls:

• Guards (6): Zach LaVine, Lonzo Ball, Alex Caruso, Coby White, Ayo Dosumnu, Devon Dotson (two-way)
• Wings (5): DeMar DeRozan, Patrick Williams, Derrick Jones Jr., Troy Brown Jr., Javonte Green
• Bigs (3): Nikola Vučević, Tony Bradley, Marko Simonović

© Nuccio DiNuzzo/Chicago Tribune Joakim Noah with Derrick Rose at the conclusion of their team's 114-107 win over the 76ers.

We begin this edition of the Bulls mailbag with a look at the latest player they have been connected to in free agency.

What do you think about the Bulls being interested in Paul Millsap? His numbers are still very good. Can he be a key rotational piece still? — @buzzontap

I like the fit. Even at 36, Millsap was a solid rotation player for the Denver Nuggets last season, averaging 9.0 points and 4.7 rebounds in 20.8 minutes per game. He’s a 15-year veteran who has been around winning teams and can knock down a 3-pointer (34.3% last season).

I wouldn’t move Patrick Williams out of the starting lineup for Millsap, but the Bulls need another reliable true power forward in the rotation. While the Lauri Markkanen sign-and-trade last week made sense for both him and the Bulls, his departure left the team thin in the frontcourt (although Jones could line up at power forward). Plus, Millsap would bring strong defensive tendencies and instincts, traits the Bulls could use more of.

© Nuccio DiNuzzo/Chicago Tribune Joakim Noah reacts after grabbing a rebound in front of the 76ers' Henry Sims during the second half.

However, Millsap might be the best free agent remaining on the market, and other suitors such as the Brooklyn Nets and Golden State Warriors would give him a better chance at a championship.

© Chris Sweda/Chicago Tribune Derrick Rose and Joakim Noah warm up before Game 1 of the Eastern Conference quarterfinals against the Bucks.

Is it likely the Bulls could use their traded player exception to entice Paul Millsap to sign? — Megann H.

One advantage the Bulls have in the Millsap pursuit is they should be able to pay him more than the other teams competing for his services. Millsap is an unrestricted free agent, so the Bulls wouldn’t be able to dip into that trade exception to sign him, plus they wouldn’t want to. It’s a $5 million trade exception that could be better used in a potential midseason trade to add a player, which is why their preseason roster is likely to max out at 14.

© Brian Cassella/Chicago Tribune Joakim Noah and the Bucks' John Henson scuffle in the first half of Game 2 at the United Center.

What the Bulls do have at their disposal to offer Millsap is their biannual exception, worth about $3.7 million. The other teams in the running can offer Millsap only the league minimum, so while the Nets and Warriors might offer a chance at a deeper playoff run, the Bulls at least have a financial edge.

© Armando L. Sanchez/Chicago Tribune Joakim Noah reacts to a referee's call during the second half of Game 3 against the Bucks.

Update: Millsap will reportedly sign with the Brooklyn Nets.

Video: Bradley Bozeman: What Ravens fans should know about RB Ty'Son Williams (NFL)

Any chance they sign DeMarcus Cousins ? — Eddie G.

I hadn’t thought about this one, maybe because I’ve considered Cousins cooked for a couple of years now. I know he got some minutes for the Los Angeles Clippers in this year’s Western Conference finals, but I’m not sure what you’re getting here.

© Armando L. Sanchez/Chicago Tribune Joakim Noah drives the ball past the Bucks' Ersan Ilyasova during the first half of Game 3.

If the Bulls strike out on Millsap, it makes more sense to check in on LaMarcus Aldridge, who reportedly is considering a return should his health allow it. But if they strike out on both of those options, maybe they would pivot to Cousins. Have you seen this offseason? I’m not ruling out anything.

How do you see the rotation minutes playing out once Coby White comes back? — Mike H.

© Armando L. Sanchez/Chicago Tribune Joakim Noah stands by the bench after the Bulls lose Game 4 to the Bucks.

Of the many things I’m interested in going into training camp, where White fits into this team — and, ultimately, into the Bulls future — is right at the top.

Overall, the Bulls additions have a chance to be a positive development for White. He was much better toward the end of last season when he played off the ball more frequently and got a higher percentage of catch-and-shoot opportunities. The guard rotation looks crowded, but he’s going to play a huge role as a reserve. He might be better suited as instant offense coming off the bench anyway.

© Armando L. Sanchez/Chicago Tribune Joakim Noah goes up for a basket during the second half against the Bucks in Game 4.

I would guess the Bulls will be most effective staggering Zach LaVine’s and DeMar DeRozan’s minutes, keeping one of them in the game at all times, and White should get paired with defensive-minded Alex Caruso often in some three-guard lineups. These should all play to his benefit, and I think White will accept the change in his role.

© Brian Cassella/Chicago Tribune Joakim Noah reacts to missing a shot in the second half during Game 5 at the United Center.

I’m not sure where this ultimately leaves White. It’s not for nothing that the front office held on to him after turning over virtually the entire roster, and it doesn’t appear his name came up much in any credible trade conversations. But if the Bulls had a ton of faith in him, they wouldn’t have seen a need to add so many guards.

Once he gets healthy, I think White will get a lot of minutes. Whether he can be productive and more efficient in those minutes will be the key to whether he sticks around going forward.

What’s the latest regarding last year’s roster of players? Are they all out of a job now? I know Coby White is on the mend, but Ryan Arcidiacono, Denzel Valentine and others? — Roderick L.

Only two players — Zach LaVine and White — remain from the roster in April 2020, when Artūras Karnišovas took over basketball operations. So the short answer is yes, in one way or another, everyone else is gone.

But there wasn’t much fanfare for some of these departures, especially the players who have not found new teams.

After the Bulls Denzel Valentine to a one-year deal as a restricted free agent a year ago, he became an unrestricted free agent this summer, and there never seemed to be much consideration about bringing him back.

The Bulls declined a $3 million team option on Arcidiacono, which made him an unrestricted free agent. There were rumors about the Bulls potentially bringing him back on a minimum deal, but their guard rotation has grown crowded. Adding depth in the frontcourt seems more likely.

If fans will be allowed into the UC next season (with all safety protocols intact, of course), will the new management find a night to honor Joakim Noah for all his gutsy blue-collar work as a Bull? And for just that game, will the team have to shoot FTs a la Jo? — Michael L.

© Brian Cassella/Chicago Tribune Joakim Noah and the Bucks' Michael Carter-Williams go for a rebound in the first half of Game 5 at the United Center.

I love it. My only addition is they should honor Noah during a game against the Cleveland Cavaliers.

Noah did come to the United Center for a game last season, sat near the owner’s suite with COO Michael Reinsdorf and got honored with a video tribute after the first quarter. But that was paltry compared with the reception he would get with fans back at the UC. I hope the Bulls make it happen.

• Sign up for alerts on your phone, desktop and inbox to stay current with the latest news
• Sign up for our sports newsletter, delivered daily each morning

< PREVIOUS SLIDE SLIDE 1 of 8 NEXT SLIDE >

The Pistons' Marcus Morris guards Joakim Noah during the first half at the United Center.

© Armando L. Sanchez/Chicago Tribune