Barcelona have been strongly linked with a move for the Frenchman in recent months, with the Catalan outfit identifying Mathieu as their main defensive target this summer.
However, Barca are unprepared to pay Mathieu's release clause – which stands in the region of £17m – a figure that Salvo is demanding before sanctioning a move.
"Mathieu is a Valencia player and he'll only leave Valencia if his clause is paid. He's one of our captains, he's very important to us and we don't have any cover for his position," Salvo said in a statement.
"Selling him would mean we'd have to cover his loss with a player of the same standard. If FC Barcelona don't pay his release clause, he will remain a Valencia player."
Mathieu has a contract with Valencia until 2017.