Athletic Bilbao president Josu Urrutia says a new contract offer has been made to Kepa Arrizabalaga.
The goalkeeper is a January target for Real Madrid.
“We are aware of what is being said in the media and until he tells us that he doesn't want to renew, then all signs so far have been positive," said Urrutia.
“We have explored every single avenue, every possibility to ensure that Kepa stays here with us and we hope that he will do the same."
On Real Madrid, he added: “They have not contacted us but we know about the rumours which have been circulating. As far as we are aware, Kepa hasn't received any offers - that's what his agent has told us.
“If Kepa decides to leave, he must put in a transfer request and deposit his buy-out fee. The process of coming to an agreement with Kepa has been going on for the past 15 months."