United on Monday made a bid for the former Arsenal captain, who has failed to secure a regular starting spot at Barca since returning to the club from the Gunners two years ago.
However, Barca insisted the 26-year-old midfielder was not for sale and Vilanova has now confirmed that Fabregas is not wanting to move on either.
Vilanova said at a press conference on Tuesday morning: "I’m aware there have been offers, I had a conversation with him and he told me that he wanted to continue here and that he didn’t want to go to another big club.
"He wants to succeed here."
Confirmation that Fabregas is committed to the club will come as a boost to Vilanova following the departure of rising star Thiago Alcantara.
The Spain international is currently finalising his move to Bayern Munich after the European champions reached an agreement with Barca last weekend to sign the 22-year-old for a fee which could rise to 25million euros (£21.6m).