Per ESPN.com's Zach Lowe, Rockets general manager Daryl Morey is "likely" to go after James after the 2017-18 season.
The Rockets have emerged as one of the most talked-about suitors for James next offseason.
Lowe noted new Rockets owner Tilman Fertitta previously stated he would pay into the luxury tax to keep his team as a top contender for an NBA championship.
James can opt out of the final season of his three-year deal with Cleveland after this season. The four-time NBA MVP is averaging 28.4 points, 9.2 assists and 8.2 rebounds per game. He has led the Cavs to a 24-9 start this season, one game behind the Boston Celtics for the best record in the Eastern Conference.