The Frenchman is a target of the Spanish giants and Barca sporting director Andoni Zubizarreta this week confirmed that a bid had been made.
With Carles Puyol having retired, Mathieu is among Luis Enrique's targets for his maiden campaign in charge of the club.
Mathieu insists that he does not want to force the situation or provoke an exit, but described a potential move to Camp Nou as a "big step" in his career.
"This statement is... to tell the truth about the situation and not feed the rumours and speculation that has come up in the past several days," he said in a message released via Spanish news agency EFE.
"Valencia has an offer on the table from a very important club. I won't hide from the fact that this would be a big step in my career.
"I came to Valencia on a free transfer five years ago, and this transfer would be beneficial to all parties involved. I think it's time to take the next step and close the chapter on a team that I hold so deeply in my heart.
"I want to deny the accusations that have been made against me, that I am rebelling and that I refuse to work with the team."
Mathieu made 32 league appearances as Valencia finished eighth last season.
