Jose Mourinho hopes the £89million midfielder will be fit for the trip to Anfield on October 14.
Pogba hobbled off the pitch in last night's 3-0 Champions League win over Basel and was seen leaving Old Trafford on crutches.
A scan carried out at United's Aon Training Complex today confirmed Pogba faces a month on the sidelines.
Mourinho is understood to be willing to bide his time with the France star's recovery.
He is taking a similar approach to the return to health of Zlatan Ibrahimovic.