Nazr Mohammed suffered a sprained middle finger on Monday and is questionable to return.
The Bulls and Nazr Mohammed have verbally agreed to a one-year contract at the veteran's minimum, according to CSN's Aggrey Sam.
Tom Thibodeau said he'd like to have Nazr Mohammed return next season.
Nazr Mohammed said he isn't expecting further punishment from the league office after being ejected Friday night.
Nazr Mohammed was ejected from Friday's game for shoving LeBron James after the whistle.
Nazr Mohammed will start for the Bulls on Wednesday and Marco Belinelli will come off the bench.
Nazr Mohammed double-doubled vs. the Raptors on Friday with 16 points and 13 boards, adding one steal and one block in 43 minutes.
Nazr Mohammed started in place of injured Joakim Noah (foot) and had six points, 10 rebounds and a block in Tuesday's loss.
Nazr Mohammed blocked three shots with 11 rebounds in Friday's win over the Magic.
Nazr Mohammed played 37 minutes against the Nets on Thursday, blocking three shots to go with four points, nine rebounds and one assist.
Naz Mohammed had season highs with 12 points, 12 boards and 36 minutes during Tuesday's 90-86 loss to the Wizards, adding one block on 5-of-12 shooting.
Nazr Mohammed made a rare start with Joakim Noah (foot) out on Saturday, scoring 11 points with seven rebounds, three assists and one block vs. the Pacers.
Nazr Mohammed had 13 points, 12 rebounds and a block off the bench in Tuesday's preseason win over Memphis.
Bulls sign C Nazr Mohammed.