A decision is expected Friday, sources told ESPN.com, with the Bulls and Amundson's agent, Mark Bartelstein, scheduled to talk about specifics.
The Bulls are looking for an extra big man with Taj Gibson sidelined by a sprained left knee. And Chicago has just enough room under its hard salary cap of $74.307 million to sign Amundson, who is eligible to play for the Bulls in the postseason because he was waived by Minnesota before Friday's 11:59 p.m. ET deadline.
Amundson has been looking for a new team since Feb. 8, when the high-energy big man secured his release from the Minnesota Timberwolves after seeing his playing time cut.
Amundson told Fox Sports Florida earlier this week that the Miami Heat have also considered him for a roster spot. He also told the network that the Wolves, before letting him go, talked with Philadelphia about a potential trade sending point guard Luke Ridnour and Amundson to Philadelphia for center Spencer Hawes before deciding that dealing Ridnour could leave them too thin at point guard with Ricky Rubio working his way back to full strength following knee surgery.
Amundson, in his seventh NBA season, has career averages of 3.8 points and 3.6 rebounds.