The Orange County Register reported that the committee made its recommendation on a 5-1 vote, with Kansas City Chiefs owner Clark Hunt opposing the recommendation.
Any move must be approved by 24 of the NFL's 32 owners. The committee's recommendation does not guarantee approval of the project by the full ownership, which is meeting in Houston to discuss the matter.
St. Louis Rams owner Stan Kroenke, meanwhile, has proposed to build a $1.86 billion stadium in Inglewood, California.
Earlier Tuesday, the league made a presentation on the stadium proposals in the home markets of San Diego, St. Louis and Oakland, clearing the way for all three teams to be eligible to move.
The Rams presented their project on Inglewood first, followed by the Chargers and Raiders -- which included Disney CEO Bob Iger, who is a consultant to the group. The NFL made the final presentation.
Disney is the parent company of ESPN.
NFL panel backs Carson proposal
Michael Eaves and Andrew Brandt explain the NFL's six-owner committee on L.A. opportunities recommendation of the Chargers and Raiders' Carson project.