While Bosh reportedly would prefer to stay with James in Miami, Bosh reportedly has a four-year, $88 million max deal with the Rockets lined up as a fallback option.
The Rockets would need to clear cap space to sign Bosh, potentially by unloading center Omer Asik and guard Jeremy Lin in trades. Houston has already agreed to a potential trade with New Orleans involving Asik, and a trade that would send Lin to Philadelphia is in the works, according to ESPN.com.
The team may need to move quickly, as it will not have enough room under the cap to sign Bosh if it first matches the three-year max offer sheet Chandler Parsons signed Thursday with the Dallas Mavericks.
Houston has three days to decide whether to retain Parsons by matching the offer sheet. The Rockets have reportedly had talks with other small forwards, including Luol Deng, Trevor Ariza and Paul Pierce.
If the Rockets sign Bosh before the window for matching Parsons' offer sheet expires, they plan to match, according to Jonathan Feigen of the Houston Chronicle. However, if Bosh opts to remain in Miami, Houston has not decided whether it will keep Parsons.
In 79 games last season, Bosh averaged 16.2 points and 6.6 rebounds while helping Miami reach the Finals, where they were beaten by San Antonio in five games.
The nine-time All-Star exercised the early termination option on his six-year, $110 million contract last month to become an unrestricted free agent.