"I'm outta there," Jones said when reached by telephone by Shannon Sharpe on the network's "Undisputed" show.
Jones had been the subject of trade talks recently after general manager Terry Fontenot said the team would be taking calls about the former All-Pro receiver last month.
Jones, 32, requested a trade from the Falcons at the beginning of the offseason in March, but the organization was trying to protect him and work quietly behind the scenes, a source told ESPN's Adam Schefter, and has been talking to other teams for weeks. The Falcons prefer not to trade him in the NFC but would do so for the right price, the source said.
Atlanta has asked teams that have inquired about Jones for a first-round draft pick in return, sources told Schefter.
When Jones was asked by Sharpe where he would like to go play, he said he would like to play for a winner.
"Right now I wanna win," Jones said.
Jones, whose base salary of $15.3 million is fully guaranteed for this season, is scheduled to cost the Falcons $23.05 million against the cap in 2021 and has cap hits of $19.263 million in 2022 and 2023. If the Falcons move Jones after June 1, the move would offer Atlanta relief against the cap this season because the dead money owed to him would be split between this season and next.
Jones has played 10 seasons with the Falcons, who selected him sixth overall in the 2011 draft, leading the NFL in receiving twice (1,871 yards in 2015 and 1,677 yards in 2018) and three times in yards per game (2015, 2016 and 2018). He made seven Pro Bowls and was named first-team All-Pro in 2015 and 2016.
He became one of the faces of the Falcons, starting 134 of the 135 games he played in and making 848 catches for 12,896 yards and 60 touchdowns. He's the Falcons' all-time leader in receptions and receiving yards and second to Roddy White in receiving touchdowns (63).
Jones, though, had one of his worst seasons in 2020, limited to nine games due to injury with 51 catches for 771 yards and three touchdowns. While his 15.1 yards per catch was his highest since 2017 and his catch percentage of 75% was the best of his career, his 85.7 yards per game was his lowest since 2012, his second year in the league.
The Falcons did make one receiver move Monday, signing receiver Tajae Sharpe. The 26-year-old spent four seasons in Tennessee with Arthur Smith, now the Falcons' head coach, from 2016 to 2019, where he caught 92 passes for 1,167 yards and eight touchdowns. He spent 2020 with Minnesota, where he played in four games with no catches.