Appearing on Thursday's episode of The Herd with Colin Cowherd, Bosh predicted James will sign with the Rockets "because it's like the next Avengers movie."
James' future will be the dominant topic of the offseason, which could begin as soon as Friday if the Golden State Warriors complete a sweep of the Cleveland Cavaliers in the NBA Finals.
The four-time NBA MVP can opt out of his deal with the Cavs to become a free agent.
If James' sole concern is winning a championship, Houston would be a logical fit. The Rockets won an NBA-high 65 games during the regular season and took the Warriors to Game 7 in the Western Conference finals.
ESPN's Adrian Wojnarowski said on Friday's edition of The Woj Pod (h/t Shane Mickle of ClutchPoints.com) that Chris Paul, who is going to be a free agent, isn't likely to give Houston a discount on his next deal.
The Rockets don't have a lot of financial wiggle room this offseason. They have $86.9 million in salary commitments to six players next season before factoring in what an extension for Paul will add, per Spotrac.
Per Basketball Insiders' Eric Pincus, the NBA salary cap for 2018-19 will be $101 million with the luxury tax cap at $123 million.
James and Bosh helped usher in the NBA's superteam era when they partnered with Dwyane Wade to lead the Miami Heat to two championships in four seasons together from 2010-14.
In 15 seasons, James has only played for teams in the Eastern Conference. A potential move to Houston would force him to go through the Warriors to reach the NBA Finals, but it could present him a chance to play alongside Paul, assuming he re-signs, and James Harden.