Liverpool midfielder Philippe Coutinho could be out for the rest of January after injuring a hamstring in the League Cup win against Stoke.
Defender Dejan Lovren also suffered a similar injury and Kolo Toure cramp, but both have shorter recovery times.
The Reds face Exeter in the FA Cup third round on Friday (19:55 GMT).
"Phil's is more serious than Dejan and Kolo but none of these players will be available on Friday," said manager Jurgen Klopp.
"Kolo should be available next week, Dejan will be available after Manchester United. Phil needs one or two weeks longer."
Six Reds players – Coutinho, Lovren, Martin Skrtel, Jordan Rossiter, Divock Origi and Daniel Sturridge – are out with hamstring injuries.
And with Mamadou Sakho also sidelined, the Reds do not have a senior central defender available to face Exeter.