On Friday, TMZ Sports provided comments from the six-time Pro Bowl selection about the potential of adding Brown to the Falcons' already high-powered offense.
"Nah, man. We tight over here," Jones said. "We good over here."
Atlanta ranked fourth in passing yards per game and sixth in total offense in 2018. Jones, Mohamed Sanu and Calvin Ridley, the team's top three receivers, all remain under contract for next season.
So, while Jones and Brown could create one of the best pass-catching tandems in NFL history, the Falcons are likely better off focusing their attention to other areas of the roster during the offseason.
Atlanta finished the campaign 28th in total defense and 20th in takeaways. Struggles on that side of the ball were the main reason for the team's 7-9 record and a first playoff-less season since 2015.
Meanwhile, questions about Brown's future were amplified Thursday when Steelers President Art Rooney II told Gerry Dulac of the Pittsburgh Post-Gazette it's "hard to envision" the two-time NFL leader in receiving yards remaining on the roster by the time training camp arrives.
"There's not much we can do right now; we have time to make a decision," Rooney said. "We'll look at all the options. We're not going to release him, that's not on the table. But I will say all other options are on the table."
Brown missed the Steelers' Week 17 game against the AFC North rival Cincinnati Bengals following a rumored dispute with quarterback Ben Roethlisberger.
The Arizona Cardinals, Baltimore Ravens, Buffalo Bills, New York Jets, San Francisco 49ers, Tennessee Titans and Washington Redskins are among the teams with wide receiver at or near the top of their to-do list heading into the offseason.