There is still "skepticism" a deal will get done before the March 25 deadline considering Drummond's $28.7 million salary this season.
The Cavaliers have been holding Drummond out of games since mid-February in the hope of dealing him.
There is no denying Drummond's impact on the court, with averages of 17.5 points, 13.5 rebounds, 1.6 steals and 1.2 blocks per game in 2020-21.
The two-time All-Star has led the NBA in rebounding four different times, while he would rank second in the league this year with enough games to qualify.
His 4.7 career offensive rebounds per game would be especially valuable for any contender, including a Bulls team that ranks 19th in the league in offensive rebound percentage this year.
Wendell Carter has had strong performances at center for Chicago, but the squad has few alternatives down low with Thaddeus Young and Lauri Markkanen used at times out of their natural positions.
With a 16-18 record entering Thursday, the Bulls are in the mix for a playoff spot for the first time since 2017, and a veteran like Drummond could help put the team over the top. The key for the franchise is ensuring not to sacrifice too much with an emerging young core around Zach LaVine.