Off contract in June, Valverde is on track to run down his contract and leave San Mames at the end of the season.
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As such, Athletic president Jon Uriarte and his fellow directors are now preparing to move for a successor.
Top of Uriarte's shortlist is Bournemouth boss Andoni Iraola. The former Rayo Vallecano has proved his qualities in England, though has so far not been offered a move to a bigger club.
Instead, a return to LaLiga and Athletic will be put in front of him in the coming months, though he isn't Uriarte's lone target.
Elche's Eder Sarabia is also being considered as he and his team continues to stun LaLiga experts after their return to the top-flight this season.