The Spanish shot-stopper has struggled to make an impression when handed opportunities this season and could even be the club’s third choice goalkeeper if he stays.
His deal runs out in the summer, but Reds boss Jurgen Klopp is happy to see his stay at the club extended.
It is claimed that if the 34-year-old does want to stay at Liverpool then he will have to pen a contract on a lower salary than he takes home at present.
Adrian has enjoyed life on Merseyside, but has continued to be linked with a potential return to Spain at some stage.
The custodian made 32 appearances in La Liga for Real Betis and could be of interest to Spanish sides in the summer.
And it remains to be seen if Adrian would be happy with potentially becoming the third choice goalkeeper at Liverpool.
He has kept one clean sheet in the Premier League this season.
