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.
Sam Amick of USA Today started the James-to-Houston discussion on Dec. 9 when he reported the Rockets' "strong belief" is they have a realistic chance to sign him away from the Cleveland Cavaliers.
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.
The Rockets will also have to re-sign Chris Paul this summer to keep him in the backcourt with James Harden.
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.