"I go to see the surgeon on Monday and if everything goes well I could return playing in three weeks," said Ledley.
Cardiff born Joe is out of contract in the summer and talks about his future will be something the club will want to sort out.
"Once he can start running we're looking at three weeks all being well," said Dave Jones.
"So some time in April we might have him back. With Joe, I'm trying to push the physios to force it along but they might tell me five weeks. It's just down to Joe.
"We've got to get the all-clear that he can start running and once he starts running, hopefully we can push him along. But it's still an injury that will take the timescale the specialist has given.
"I think Joe wants to play again before the end of the season."
Ledley's last game was the 6 - 0 away win over Bristol City in January.
