The veteran goalkeeper signed a new two-year contract at Anfield last summer but has played just once this season and is firmly the third-choice goalkeeper in the Reds squad.
He still has a year left on his contract and the Spaniard wants to assess his options once the campaign ends with the Champions League final on Saturday.
The 35-year-old stressed that he is open to discussing a move away with Liverpool if he gets an interesting offer as he feels that he still has a lot to contribute going forward.
Adrian told Spanish sports daily Marca: “When the season ends, we will have put all the pros and cons on the table.
“If an interesting offer arrives and fills me with hope, I have it in my mind to discuss it with Liverpool.
“I think I still have a lot to contribute, on and off the pitch.”
The Spaniard admitted that a move back to Spain has its appeal but pointed out that he has almost spent his entire career in England.
Adrian indicated that he is open to staying in England even if he leaves Liverpool this summer.
Asked if he wants to return to Spain, he said: “I would not say yes or no.
“I made my debut at Betis, but I came to the Premier League in 2012 and I have spent almost my entire career here.
“The homeland pulls, but I would not mind staying in England.”
