Carragher, speaking to the club's official website, revealed the good news concerning himself and his Anfield colleague.
"I'm probably a couple of weeks ahead of where we thought I'd be at this stage. The physio is pleased so I just hope it keeps progressing that way. I will be back sometime in January. Early January if it all goes well," said Carragher.
"That's back in the first team hopefully, and I'll be back training for a good month before that and play in a couple of reserve games.
"Milan Baros is doing really well too and he will be back way before me. He's had his cast off for a while now. I'm not doing much with him as I'm mainly in the gym and the pool. He's doing a bit in the pool, and a lot of jogging outside."