"It was a difficult decision because Omer did a nice job for us," Bulls general manager Gar Forman told the team's website Tuesday. "Matching the offer for Omer could have put us in a difficult position going forward in trying to acquire high-level talent. We wish Omer good luck and continued success."
The deal that the Rockets structured would have meant the Bulls would have been on the hook for a cap hit of almost $15 million in the final year of the contract. The Bulls decided they did not want to absorb such a substantial penalty, given their current cap situation.
Asik averaged 3.1 points and 5.3 rebounds coming off the Bulls' bench.
The 6-foot-5 Belinelli, a former first-round pick (18th overall) by Golden State, averaged 11.8 points last season with the New Orleans Hornets.
Mohammed is expected to sign for the veteran's minimum, which is $1.3 million.
The Bulls also officially announced the signing of Kirk Hinrich, who had a news conference Tuesday afternoon.
The Bulls signed veteran Vladimir Radmanovic earlier this week.
ESPNChicago.com's Nick Friedell contributed to this story.