Sources told NFL Network that Jones wants an "update" to his contract.
Jones, 29, has not been with the Falcons this offseason for voluntary workouts. He is set to make $10.5 million this season. He signed a five-year, $71 million contract extension in 2015.
The two-time All-Pro and five-time Pro Bowl selection had 1,444 yards and three scores on 88 receptions in 16 games in 2017. Jones had 1,409 yards and six scores on 83 receptions in 2016. In 2015, he led the league with 1,871 yards and 136 receptions. He also scored eight touchdowns that season.
Jones was also absent for the majority of OTAs last offseason. He sparked rumors this offseason when he deleted all ties to the Falcons from his Instagram account and was seen working out with Terrell Owens.
The entire offseason program is voluntary, until a three-day minicamp, which is from June 12 through June 14.
Jones' cash payout for 2018 ranks behind Sammy Watkins, Jarvis Landry, Mike Evans, Antonio Brown, Allen Robinson, DeAndre Hopkins, Paul Richardson, DeSean Jackson, Larry Fitzgerald, T.Y. Hilton and A.J. Green, according to Spotrac.