It has been suggested that Manchester City are preparing a big-money move for the 26-year-old, who has struggled with injury this season.
However, Faus has reiterated that the Argentine is not for sale in the summer.
"Leo is not in danger of leaving," he told RAC1.
"[President] Josep Maria Bartomeu said it, he said it and all of the directors have said it. He wants and we want to continue together."
Messi also recently claimed that he wanted to retire at the Camp Nou.