"I'm out of there man," Jones said. "I want to win."
Photos surfaced on Jones on Friday on social media that showed the wide receiver wearing a Cowboys sweatshirt.
"I ain't going to Dallas. I never thought about going to them," Jones said Monday.
Jones, 32, was limited to nine games last season due to a hamstring injury. He pulled in 51 receptions for 771 yards and three scores. The seven-time Pro Bowl selection and two-time All-Pro recorded 1,394 yards and six scores on 99 catches in 15 games in 2019. Jones led the NFL in receiving yards in 2015 and 2018.
He signed a three-year, $66 million contract extension with the Falcons in 2019. He is under contract through 2023.
The Falcons received trade calls for Jones earlier this off-season. Owner Arthur Blank and general manager Terry Fontenot fed into speculation of a potential Jones trade this spring when they left the door open for a potential move.
Blank said he didn't know if Jones or quarterback Matt Ryan still would be with the team within the next two or three years.
The Baltimore Ravens, San Francisco 49ers, New England Patriots, Los Angeles Chargers, Tennessee Titans, Indianapolis Colts and Green Bay Packers are among the favorites to acquire Jones if he is traded.