At least six players have already indicated they will not play for Cameroon at the 2017 Africa Cup of Nations (AFCON) finals in Gabon come January.
Matip has established himself as an important part of Jurgen Klopp's side since arriving from Schalke 04 on a free transfer in the summer.
This leaves Broos and the Cameroon FA, Fecafoot, with a significantly weaker selection, and in a statement released on Tuesday, they suggested they could "take action" against those to opt out.
The other five Cameroon players are Andre Onana (Ajax Amsterdam), Guy N'dy Assembe (Nancy), Maxime Poundje (Girondins Bordeaux), Andre-Frank Zambo Anguissa (Olympique Marseille) and Ibrahim Amadou (Lille).
"Joel Matip does not want to play with the Lions at the moment due to a bad experience with the previous technical staff".
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Matip is one of seven Cameroon players to have pledged not to travel to Gabon in January - also including West Bromwich Albion's Allan Nyom - and national manager Hugo Broos has pledged to do what he can to ensure they face sanctions for the move.
Matip has insisted on continuing his self-imposed exile from worldwide football after his bad experience with the previous Indomitable Lions coaches, while Onana, Assembe, Nyom have put club before country so as to maintain first-team places at their various clubs.
"These players have put personal interest above those of the national team", Broos said.
That is unlikely and Press Association Sport understands Liverpool believe there are no issues which are likely to affect Matip's availability over the coming month other than fitness, as the defender has missed the last two matches with an ankle injury.