Valencia's president Amadeo Salvo has insisted that the French defender will only be leaving the club if his buyout fee, understood to be set at €20m (£15.8m), is met
The Blaugrana have reportedly made 30-year-old Mathieu one of their top targets in their search for new defensive options, with the player himself believed to be keen on a switch.
Salvo, however, is adamant he will not negotiate over the transfer fee, telling Barca to match the player's €20 million (£15.8m) release clause if they wish to open talks with him.
"Mathieu is a Valencia player and he'll only leave Valencia if his clause is paid," said Salvo at a press conference presenting new head coach Nuno Espirito Santo.
"He's one of our captains, he's very important to us and we don't have any cover for his position. Selling him would mean we’' have to cover his loss with a player of the same standard.
"If Barcelona don't pay his release clause, he will remain a Valencia player."
Mathieu, who joined Valencia in 2009, is currently under contract at the Mestalla until 2017.