The former Arsenal captain, who returned to Barca in the summer of 2011, was the subject of a 30 million euro (£26m) offer from United on Monday.
Subsequent reports suggested the midfielder could be open to the transfer, but only if Barcelona actively wanted to remove him from the wage bill at Camp Nou.
However, only Victor Valdes started more games than Fabregas for Barcelona in La Liga last season and coach Vilanova says it is the player’s wish to remain at the club.
"I know he has received offers from other teams," Vilanova said.
"But Cesc has told me he wants to stay here. He has told me it is his dream to stay with Barcelona.
"He doesn't want to go to other teams for money reasons or playing time. He knows there is competition for places here, but his decision is to stay. I am relaxed about the situation.
"It is a good sign that the club gets offers for our players. It shows we have players other teams want. But Fabregas wants to stay."