The Rockets have made a maximum offer to Bosh of four years, $88 million, according to sources.
The Rockets traded guard Jeremy Lin and a future first-round pick to the Los Angeles Lakers on Friday, a league source told ESPN's Jeff Goodman. After trading Lin, the Rockets' plan now is to complete their agreed-upon trade of Omer Asik to the New Orleans Pelicans.
Bosh, since opting out of the final two years of his deal -- worth $42 million -- with the Miami Heat, had planned to see what James decided before making his choice.
Bosh would give the Rockets a big forward with 3-point range, making him the the ideal frontcourt sidekick to pair with All-Star center Dwight Howard.
The Dallas Mavericks signed Rockets small forward Chandler Parsons for a three-year offer sheet worth in excess of $45 million Thursday but Houston plans to match the offer, sources told ESPNDallas.com's Tim MacMahon.
Houston has until 11:59 p.m. Sunday night to match the Mavs' offer to Parsons, who currently accounts for a $2.9 million hold on the Rockets' cap. The Rockets can exceed the cap to keep Parsons.
ESPN The Magazine's Chris Broussard contributed to this report.