According to the Fort Worth Star-Telegram, Jones was scheduled to speak to several Dallas-area media outlets on Sunday, but told them that he would not answer questions about the anthem policy.
Jones said last week that the Cowboys will stand on the field during the national anthem this upcoming NFL season.
"Our policy is you stand during the anthem, toe on the line," Jones said.
Stephen Jones, who is the son of Jerry and the team's executive vice president, said the players will stand "if they want to be a Dallas Cowboy."
The NFL and the NFL Players' Association "have come to a standstill agreement on the NFLPA's grievance and on the NFL's anthem policy," the two sides said in a joint statement on July 19. They added that no new rules would be "issued or enforced for the next several weeks."
In May, NFL owners voted on a new national anthem policy, removing a requirement for players to be on the field for the anthem, and giving the players the option to stay in the locker room.
Teams who did not adhere to the policy and "do not show proper respect for the flag and anthem" on the sidelines were subject to fines.
The anthem issue has been a divisive one, with some feeling that players who don't stand for the song are being disrespectful to, among others, the U.S. military. Others feel it is within the players' rights to protest perceived social injustice peacefully.
Former San Francisco 49ers quarterback Colin Kaepernick started the movement in 2016 to kneel during the national anthem as a protest to perceived police brutality against African-Americans, social injustice and racial inequality.
Kaepernick and former 49ers safety Eric Reid have both filed collusion cases against the league after failing to land jobs as free agents.