Some reports have even suggested that the Spanish coach has already turned down the chance to move to Camp Nou this summer, with current boss Gerardo Martino expected to be sacked even if he leads the Blaugrana to the Liga title.
However, Valverde insists that not only has not spoken with Barca, he has no intention of doing so, insisting that he is perfectly happy at San Mames.
"I have not rejected any offer because I have not received any offers because I have a contract with Athletic," the 50-year-old told reporters.
"The only way I would leave the club is if Athletic asked me to leave, which I don't think would happen, or if I asked to leave, and that definitely won't happen.
"As you see, there is no possibility of me leaving Athletic. These are just rumours, we ignore them and move on. I shouldn't have to keep clarifying this."
Luis Enrique is currently the favourite to replace Martino as Barca boss, should the Catalans decide to dispense with the services of Martino after just one season at the helm.