The move was expected, as Jones sat out the required eight games after being placed on injured reserve. He returned to practice Wednesday and is eligible to play Sunday game against the Dallas Cowboys.
Falcons coach Dan Quinn, however, did not immediately commit to re-inserting Jones back into the lineup.
"We'll stay in the same format as we had last week, and as we go through the week, we'll take it step by step to see where he's at,'' Quinn said Monday. "Too early to make a prediction and where he could be. I know he's eligible to be back this week. That doesn't mean he's ready to. So we'll put him out there when he's 100 percent ready."
Quinn previously said he wants Jones to pass all the necessary markers, which includes being pain-free while running.
Asked last week if he felt any lingering pain, Jones responded, ``Not thinking about that.''
The Falcons lost starting safeties Keanu Neal (torn ACL) and Ricardo Allen (torn Achilles) to season-ending injuries, so getting Jones back on the field would be a much-needed boost to the unit. The Falcons had a dismal defensive performance in a 28-16 loss to rookie quarterback Baker Mayfield and the Cleveland Browns on Sunday. They enter this week surrendering 28.2 points and 414.3 yards per game.
"Him coming back, that's huge for your defense in general,'' fellow linebacker De'Vondre Campbell said of Jones. "He's the captain of the defense. He's the Mike. He's does some things really well that not a lot of people can do. Just having him back is going to be huge in general."
Jones led the Falcons in tackles the previous two seasons and has seven career interceptions.
To make room for him on the 53-man roster, the Falcons waived offensive lineman Rees Odhiambo.
The Falcons, who have placed six starters on IR this season, are allowed to designate two players to return per season. After Jones, the team could activate two-time Pro Bowl running back Devonta Freeman after groin surgery. Freeman is eligible to return for the Dec. 23 game at Carolina Panthers.