The Manchester United midfielder has been out of action since picking up the injury in November, but returned to light training this week.
The club's manager told reporters: "Michael Carrick is getting better and has started some light work back on the grass. I would still expect it'll be around another two weeks, give or take a few days either side of that.
"We're trying to hope [for Christmas], but he's not joined in any football yet. I think with the injury he's got, it's something he'll not be able to play game after game after game.
"It's just something we have to take care of. Obviously Michael is a big influence as far as what we've got in central midfield, so to lose him was a big blow."
The champions face Aston Villa in the Premier League tomorrow.