Carrick, 36, has made only one appearance so far this season in a Carabao Cup third-round clash against Burton Albion and has made Jose Mourinho's matchday squad in the Premier League just three times.
The veteran midfielder has not featured in a squad since the 1-0 win over Southampton back in late September having struggled with a calf injury – while some reports have also claimed he has been suffering from a mystery illness which baffled club doctors.
While he will not be ready for league fixtures against Brighton & Hove Albion, Watford and Arsenal, the report suggests he will be in contention to feature against CSKA at Old Trafford on Tuesday 5 December.
United will enter that final match of the group campaign still needing to seal their qualification for the knock-out stages of the competition – but only a six-goal defeat to the Russian giants will prevent them from doing that.
United were short on midfield options throughout October with both Paul Pogba and Marouane Fellaini joining Carrick on the sidelines, leaving Mourinho with the options of Nemanja Matic, Ander Herrera and Scott McTominay.
Those injury woes have eased in recent weeks, however, with Fellaini returning from a knee issue prior to the November international break. Pogba came back from a three-month layoff last Saturday to score and provide an assist against Newcastle United.
Carrick, who was awarded the captain's armband in the summer following Wayne Rooney's Old Trafford exit, is in the final year of his contract at the club.