The Steelers are targeting Woodley to return for the Dec. 19 game at San Francisco, the source added.
Woodley tweaked his hamstring in Sunday's rout of the Bengals and sat for the final three quarters. He had missed the previous three games with that injury.
The loss of Woodley decimates the Steelers' pass rush. In the four games in which he has been sidelined or failed to finish, Pittsburgh has recorded seven sacks. It's basically been a one-man pass rush without Woodley: James Harrison has six of those seven sacks during that span.
The Steelers will probably send heavy pressure at Browns quarterback Colt McCoy, who was sacked five times last year in Pittsburgh. McCoy has been one of the hardest hit quarterbacks this season. He's been sacked 29 times, fifth-most in the NFL.