Promoters Bob Arum and Richard Schaefer were to tour the new Dallas Cowboy stadium along with HBO Sports president Ross Greenburg and listen to a proposal from Jones to play host to the fight, a person close to the promotion said.
Other leading contenders are the MGM Grand hotel arena in Las Vegas and the Superdome in New Orleans.
Neither fighter has formally signed for the fight, though both have agreed in principle to terms. Promoters are so confident it will happen that they are also scouting sites in New York City for a Jan. 6 news conference to formally announce the bout.
The anticipated demand for the fight brings both the Cowboy stadium and Superdome into the equation because they can seat far more people than the MGM Grand. The Dallas stadium could hold 100,000 or more for a fight, including seats on the field.
The biggest gate in boxing history was the $18.4 million in tickets sold for Mayweather's 2007 fight with Oscar De La Hoya, and promoters believe they can get a bid of $20 million and more from one of the three contending sites.
Jones said last week he was "still desirous of looking at what we can do here with the fight" at the new $1.2 billion stadium, which landed a Super Bowl, Final Four and Notre Dame home game before it even opened.
Working against any bid by Jones is the lure of Las Vegas, where the biggest fights are usually held.