Matip, 25, was named in Cameroon's preliminary squad for this month's Africa Cup of Nations, but the defender said he did not want to play.
He would have been in the squad, maybe on the pitch so I don't think it's fair
He was not in the final 23-man squad, but the Reds are seeking "clarity" from Fifa about his availability.
Germany-born Matip has not featured for Cameroon since September 2015.
Liverpool boss Jurgen Klopp said: "In our understanding, Joel is officially retired from international football.
"The club did everything we had to do to make this clear, but up until now we couldn't get the response we need to be 100% sure he can play.
"It's pretty difficult and really frustrating. He has been in training four or five days. He would have been in the squad, maybe on the pitch [against United] so I don't think it's fair."
Matip was one of seven of their players who said they did not want to play at the tournament in Gabon, which started on Saturday and runs until 5 February.
Another, West Brom full-back Allan Nyom, also failed to received international clearance and did not feature in his side's 4-0 defeat at Tottenham on Saturday.
The Cameroon football association (Fecafoot) can ask world governing body Fifa to suspend those players at club level for the duration of the event.
Liverpool said Fecafoot has failed to confirm whether centre-back Matip - who has made 12 Premier League appearances since moving to Anfield from German side Schalke in the summer - can continue to play club football.
Liverpool withdrew Joel Matip from their squad to face Manchester United on Sunday because they are unsure about his international clearance.