It is understood that Barcelona will be on the lookout for a new manager this summer as current head coach Gerardo Martino continues to come under increasing pressure.
Valverde's work at Bilbao, who sit fourth in La Liga, has not gone unnoticed, with a number of reports linking the Spaniard with the position at the Camp Nou.
"Is my staying here negotiable? I'm flattered by the comments," Valverde told AS. "On whether it's negotiable or not, I have a contract with Athletic and I'm comfortable here."
Barcelona came from behind to beat Bilbao 2-1 on Sunday evening.