The Reds overcame Carlo Ancelotti's side at Anfield to progress in the Champions League, however it came at a cost with James Milner, Joel Matip and Alexander-Arnold all hobbling off with knocks late on.
The club confirmed on Wednesday that Matip would be out of action for six weeks with a broken collarbone, joining fellow centre-back Joe Gomez in the treatment room.
Alexander-Arnold underwent a scan on his foot after the game and whilst no confirmation has come from the club, it seems the youngster will be out of action for at least a while.
The right-back attended a promotional event on Thursday wearing a protective boot on his left foot, with speculation rife that he could also be out for up to six weeks.
He is clearly unlikely to be in contention to feature against Jose Mourinho's side. However, the hope will be that Milner can overcome his own fitness issues to replace him at right-back.
Milner was replaced by Fabinho in the 85th minute after appearing to suffer from cramps, although the manager spoke after, admitting he was unsure whether there was anything more to it.
With Gomez, Matip and Alexander-Arnold missing, should Milner also miss the game, the Reds could turn to Fabinho at right-back.
The Brazilian is a regular feature in that position for the international side and also started off as right-back at former club Monaco.
The 27-year-old is expected to leave Anfield in January, although with the spate of injuries at the back, he may be needed as a short-term solution in the coming weeks.
Liverpool will be hoping they can beat Man United for the first time in four and a half years in the Premier League, having beaten them just once home and away since Sir Alex Ferguson's retirement.