On Wednesday, Andrew Beaton of the Wall Street Journal provided sworn testimony Jones made about his conversation with Trump during a deposition for the collusion case involving former San Francisco 49ers quarterback Colin Kaepernick.
"This is a very winning, strong issue for me," Jones said he was told by Trump. "Tell everybody, you can't win this one. This one lifts me."
The Cowboys' owner added the league couldn't "piss off a large percentage of your constituency" and downplayed the overall impact of Trump's comments about the situation, per Beaton.
"Let's [not] give him that much credit," he said. "But I recognize he's the president of the United States."
Kaepernick started the movement of kneeling through the anthem in the 2016 preseason as a way to protest social injustice. Players across the NFL and other sports have followed his lead by protesting during the anthem.
"I am not going to stand up to show pride in a flag for a country that oppresses black people and people of color," he told NFL Media's Steve Wyche. "To me, this is bigger than football and it would be selfish on my part to look the other way. There are bodies in the street and people getting paid leave and getting away with murder."
Kaepernick opted out of his contract with the Niners in March 2017 and has remained unsigned since, leading him to file the collusion grievance.
Meanwhile, Trump has often given his opinion on the protests. He suggested in September that NFL owners should fire players who kneel during the anthem.
Last week, NFL owners approved a policy that requires players and staff members to either stand on the sideline or remain in the locker room for "The Star-Spangled Banner." The league will fine any organization with a player who takes a knee on the field, and the player could face team discipline under the collective bargaining agreement.