Ian Rapoport of the NFL Network provided the update Friday:
Jones opened the season with nine catches for 157 yards against the Seattle Seahawks. He tallied just two receptions for 24 yards in the Falcons' 40-39 loss to the Dallas Cowboys last week, and offensive coordinator Dirk Koetter hinted the injury was a factor.
"I think there's something to the hamstring bothering him more than he's letting on," Koetter told reporters.
The seven-time Pro Bowl selection downplayed the issue, though.
"It's football, right?" Jones said Sunday. "Everybody has nagging injuries here and there. It's nothing I can't handle."
He's proceeded to miss practice sessions Wednesday and Thursday, raising concern about whether he'll be available to face the Bears.
Normally teams would err on the side of caution at this early stage of the campaign, but the Falcons are already feeling pressure in the standings. They're 0-2, and a third straight loss to an NFC opponent would be an early blow to their playoff hopes.
Even if Jones doesn't practice Friday, the team may wait until game day to make a final decision about his status. He's capable of making an impact even if he's on a limited snap count.
Calvin Ridley and Russell Gage would still give the Falcons a solid one-two receiving punch if Jones is sidelined for Week 3. Olamide Zaccheaus would also see an uptick in playing time.
Kickoff against the Bears is scheduled for 1 p.m. ET Sunday. That's followed by a Monday Night Football clash against the Green Bay Packers in Week 4 on Oct. 5.