With Gerardo Martino likely to be replaced at the Catalan club, Valverde has been one of several names linked with the Camp Nou.
Valverde is bemused by the reports and said the only way he would leave Bilbao, who are assured a fourth-placed finish in La Liga, was if the club asked him to.
"I have not rejected any offer because I have not received any offers because I have a contract with Athletic," he told a news conference.
"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."
Valverde, who denied centre-back Aymeric Laporte was heading to Barcelona, has set his team the target of winning their final two league games.
Bilbao face Real Sociedad and Almeria to finish their campaign, and Valverde is eager to see his team celebrate earning a UEFA Champions League qualifying place in style.
"We have made history by earning the Champions League, but there is still more that we can do for our fans to enjoy the end of the season and remember this team," Valverde said.
"This group wants to be remembered for years. Our goal now is to surpass 70 points, to reach 74 points would be awesome. We want to give fans even more to cheer about on Sunday."
Arsenal prepared to replace star forward, in shock move following Saudi offer: report
'Too little, too late - Bruno Fernandes didn’t sho leadership so it’d be interesting to hear what Erik ten Hag has to say about his apology': Everything Roy Keane said about the Manchester United captain after Chelsea draw
