The Catalan club have reiterated their player will not return to the Premier League this summer
Red Devils' boss David Moyes has publically pursued the 26-year-old midfielder since taking charge at Old Trafford, but the Blaugrana have refused to budge in their stance.
And with doubts remaining over how much longer Xavi will continue to operate at the top level and Thiago Alcantara's earlier departure to Bayern Munich, Faux is adamant Fabregas remains a crucial cog at Camp Nou.
"It's a theme in sports. He has a contract, the club and the coach want him to stay," the club official told Sport.
"Come on, he will stay. The interest is real. but we have no intention of letting him go."
Pressed on the Blaugrana's own plans to sign a new centre-back, Faux confirmed the club are interested in bolstering their back four, but insisted they will not be forced into paying over the odds.
"We will prioritise the economic issue. It [the bid for a defender] will not be influenced by economics but neither will we go crazy."