They are unlikely to give clearance because that would cause an outcry in Cameroon where eight players turned down call ups for the finals in Gabon, African soccer sources told Reuters.
The Cameroon Football Federation (FECAFOOT) has made no official comment on the issue, while Liverpool are consulting their lawyers before deciding whether to play him.
Soccer's world governing body FIFA told the Merseyside club to make up their own minds on whether Matip could play, saying on Monday it had directed Liverpool to "the applicable provisions" of the regulations.
Matip was left out of the squad for Sunday's 1-1 Premier League draw at Manchester United and Wednesday's FA Cup third-round replay away to fourth-tier Plymouth Argyle because world governing body FIFA had not confirmed he was eligible.
West Bromwich Albion took the same precaution with fullback Allan Nyom for Saturday's 4-0 defeat at Tottenham Hotspur.
However, Ajax Amsterdam used keeper Andre Onana – one of the eight who decided not to play for Cameroon at the tournament - on Sunday in a 3-1 win at PEC Zwolle in the Dutch championship.
Cameroonian officials, speaking to Reuters on condition of anonymity, said it would up to FIFA to decide if any action should be taken but Cameroon had "moved on" from the matter.
Matip was called up for the finals despite having not played for the Indomitable Lions since last year's World Cup in Brazil.
"Liverpool have subsequently repeatedly sought, as a matter of urgency, clarity from FIFA in this regard," the club said.
"It is Liverpool's view that the player should be available for club football during the period of the competition and (we)will continue to work for a speedy and unambiguous resolution."
Liverpool manager Juergen Klopp said he would seek advice from the club's lawyers before using Matip.
"As you can imagine, we are in a lot of talks. We've done transfers quicker than this. It's already long term but now it's getting really tense on our side," he told British media.
"We've tried everything but at the end I have to make the decision. Of course I have to ask (Liverpool's lawyers) but the decision is for me to make. I could put him in the lineup."
(Additional reporting by Shravanth Vijayakumar in Bengaluru; Editing by Ken Ferris)
