The defender's current deal expires in June and he is out for the season due to injury.
SportsZone reports Matip has told Reds management that he wants to stay.
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However, it is unclear how Liverpool views a possible new contract agreement with the experienced centre-back.
Jrgen Klopp has previously said that he would like to keep the centre-back - but as is well known, the German will leave his role as manager at the end of the season.