Llorente has endured a frustrating campaign with Spurs, with 19 of his 22 outings in the Premier League and Champions League coming from the bench.
The Spaniard turned 33 in February, and the frontman has revealed that he is open to ending his career back at Bilbao, where he played between 2005 and 2013.
Llorente is quoted by Marca as saying: "Athletic Club are my home and if they make an offer, a return could happen. I enjoyed many wonderful moments at the club that I will never forget and Athletic will always hold a special place in my heart.
"If they do make me a proposal to come back, then I would have to think about it and yes, maybe it could happen."
Llorente has just over a year remaining on his contract with Spurs.