The 29-year-old limped out of the 1-1 draw with West Brom on 29 December with an abductor injury and has not played since.
At the time, Jurgen Klopp predicted that Matip would miss three weeks of football, which would likely keep him out of the United match.
‘The normal for this kind of injury is round about three weeks,’ said the German after the West Brom draw.
However, the Athletic report that Liverpool are hopeful he will be ready in time for the Premier League outing, going as far as saying he ‘should’ be back, on their Red Agenda podcast.
The concern will be over the possibility of rushing him back into the first team and the Cameroon international suffering another injury.
With Virgil van Dijk and Joe Gomez set to miss most, if not all, of the season, Matip has the chance to play much more regularly this season, but is struggling to stay fit.
He has made just eight Premier League appearances and two more in the Champions League, meaning Klopp has had to improvise in defence.
Inexperienced pair Nat Phillips and Rhys Williams have been called upon, while Jordan Henderson was drafted in at centre-back in the 1-0 defeat to Southampton last time out.
Fabinho, who is a midfielder by trade, has become the mainstay of central defence, performing very well but also causing the Reds to miss his presence in defensive midfield.