The midfielder has been out of action with an Achilles tendon injury since the middle of November, having made his last appearance for the Reds in the 1-0 win over Arsenal.
But with Saturday’s visit of West Ham starting a run of four Barclays Premier League games that culminates in the meeting with Tottenham on New Year’s Day, the news that the 32-year-old is making good progress has handed the boss a timely boost.
“Michael has started some work outside on grass and is getting a little bit closer,” Moyes said. “I think he’s roughly due to be back around New Year’s Day – that’s the rough time. We are hopeful we may be able to squeeze a few more days out of it but I can’t be sure yet.”
However, a back injury to Marouane Fellaini has not cleared up and Moyes is waiting to find out if this might be the time for the Belgian to undergo surgery to correct a wrist problem that has dogged the midfielder since early in the season.
“Marouane has got an injury to his back – a bit of muscle has separated from the bone in his back – which we hoped may have healed up. We’re checking it with a scan but if it hasn’t healed I might need to take a decision to get his wrist done as well. I’d hoped he'd be better in 10 days but he’s still feeling it and was not much better today [Friday].”