Nor did he seem concerned about it.
"I don't make a lot of this at all," Jones said Tuesday afternoon. "Again, my interest in San Antonio is because of how important it is to the Cowboys and our history of having training camp there and the fact that we have such a tremendous fan base in San Antonio.
"The first I heard about it, I thought it was somebody playing a joke on me about him going to San Antonio."
The San Antonio Express-News reported Davis met with several city officials on the weekend of July 18, including then-mayor Julian Castro and city manager Sheryl Sculley.
The report said the Raiders could play at the Alamodome until a stadium was built for them. The Raiders' lease at O.Co Coliseum expires following the 2014-15 season.
For an NFL franchise to change cities, it needs support from 24 of the 32 teams.
The Cowboys have held training camp in San Antonio six times since 2002. Jones has always been protective of the San Antonio market.
"What I will say is San Antonio is very important to the Dallas Cowboys," Jones said. "We have the exact same percentage of fans in San Antonio as we do in Plano, Texas -- about 98 percent.
"It would be difficult for them to make headway. I'll make sure of that. That would be very difficult. Now the Spurs are another story."