As United weigh up a third bid, his Barca coach has admitted that the final decision will lie with the player himself.
"I would prefer him to stay with us, and I dare say he will, but it's his decision," Martino told the club's official website.
"He is one of the best players in the squad. I think he will stay but there's a part that he has to decide.
"Cesc will decide the situation, but it has not occurred to me that I won't be able to count on him. If it was my decision, there wouldn't be any chance of Cesc leaving."
Fabregas scored twice as Barca beat Santos 8-0 in a pre-season friendly yesterday.