The Frenchman has developed into one of the best centre-backs in Europe over the last couple of seasons, with his performances drawing a host of glances from admiring clubs.
However, the 30-year-old has told head coach Juan Antonio Pizzi that he wants to remain with Los Che beyond this summer.
"I told Pizzi that Barcelona might come for me," AS quotes Mathieu as saying.
"I also told him that I am happy at Valencia. I feel responsible for this club and the fans."
Mathieu's release clause reportedly stands in the region of £30m.