The 29-year-old was reported to have been offered to the Catalans earlier this week, triggering speculation that he was set for a summer exit from the cash-strapped club.
Mathieu, who has a contract at the Mestalla until 2014, has now revealed he would consider a move to the Liga leaders, but added that he is happy to stay with los Che.
"Anyone would like the chance to play with a team like Barcelona but I am only thinking about one thing - Valencia," he was quoted by Sport."I am close to the final stages of my career, I am 30-years-old and I am clear with what I want to do and that is finish my career here with Valencia - this would be great."
Mathieu joined Valencia in 2009 and has been a regular feature of the side ever since.