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White, who also is nursing a sprained right ankle, pulled his hamstring during Monday night’s loss to the New York Jets.
The injury has some in the Falcons’ organization believing that White will possibly miss multiple games, the sources told Schefter.
The Falcons (1-4) also are bracing for bad news regarding Pro Bowl receiver Julio Jones, who may miss the rest of the season with a foot injury. Jones is scheduled to receive a second opinion from a foot specialist Wednesday, but Falcons coach Mike Smith said Tuesday that “the first diagnosis was not encouraging.”
White, who turns 32 next month, has been noticeably limited by his injuries this season. The four-time Pro Bowler has just 14 catches for 129 yards and no touchdowns through five games.
Atlanta already is without defensive end Kroy Biermann, fullback Bradie Ewing and linebacker Sean Weatherspoon, who all are on injured reserve. Weatherspoon was placed on short-term IR with a foot injury and is eligible to return in Week 11.
The Falcons have a bye this week before returning to action Oct. 20 against the winless Tampa Bay Buccaneers.
Information from ESPN.com Falcons reporter Vaughn McClure was used in this report.