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.

The 23-year-old opening batsman/leg spinner follows the lead of Joe Clarke, Ed Barnard, Joe Leach, Tom Fell and Ross Whiteley in extending his deal.
"We have a great bunch of lads, it's the city where I'm from and it's the club I love playing for," he said.
"I'm very passionate about the club and want to win games of cricket for Worcestershire."
D'Oliveira is the third generation of his family to play for the county, following in the footsteps of his late grandfather, former England all-rounder Basil, and his late father Damian, who served the county as player and coach.
He made his limited-overs debut against Yorkshire in 2011 and his first-class debut against Warwickshire a year later.
D'Oliveira impressed with the ball in Worcestershire's run to the T20 Blast quarter-finals, taking nine wickets, proving their most economical bowler in the competition.
His five Championship appearances in 2015 have all come since the start of July.

Police in Cornwall were called to Great Western Beach, Newquay at 17:45 BST on Tuesday.
A 38-year-old man was arrested and is in police custody.
The car had to be towed on to a different beach once the tide was out in order to remove it, an eyewitness said.
More on the car in the sea story, and other news
Jamie Clogg from Towan Motors came to help the beach owners remove the car.
He had to wait until the tide was out, after 8pm, to tow the car along the sand to Towan Beach - a journey of just under half a mile.
"The car would be stuck otherwise so I went down to help them. There were police everywhere.
"When the tide goes out there's a hard bit of ground which we could drive across - you'd never drive across the dry sand."
Liverpool withdrew Joel Matip from their squad to face Manchester United on Sunday because they are unsure about his international clearance.
[NEXT_CONCEPT]
Worcestershire all-rounder Brett D'Oliveira has signed a new three-year deal, tying him to New Road until 2018.
[NEXT_CONCEPT]
A man has been arrested on suspicion of drinking and driving after a car was driven into the sea.