Asik can't formally sign the deal until July 11, which is the first day new players can sign NBA contracts for the 2012-13 season.
The Bulls will then have three days to decide whether to match the offer or let Asik go.
Bulls general manager Gar Forman has made it clear that one of his top priorities was to re-sign Asik, but the structure of the deal could hurt Chicago's ability to keep him. The Bulls are close to the luxury tax and are wary of wading too deep into that territory.
However, Forman said after the draft on Thursday that the Bulls would be making basketball decisions, not financial ones, in reference to the salary cap.
Adding the 7-foot, 255-pound Turkish native would mark the latest move in what has been a busy offseason for the Rockets and general manager Daryl Morey.
The offensively challenged Asik averaged 3.1 points but pulled down 5.3 boards while averaging 14.7 minutes in the lockout-shortened 2011-12 season.
Information from ESPNChicago.com's Nick Friedell contributed to this report.