United on Monday made a bid for the midfielder, who has failed to secure a regular starting spot at Barca since returning to the club from Arsenal two years ago.
However, Barca insisted the 26-year-old 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 Monday 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).
Regarding Thiago, Vilanova admits he was disappointed to see him leave but understands the player's reasons as he joins former Barca coach Guardiola at Bayern.
Vilanova said: "I don't feel bad that Guardiola has taken Thiago, I feel bad that he's left Barcelona. We did everything we could for him to stay.
"I wanted him to stay here, but he knew who he was competiting against, Xavi, Cesc and (Andres) Iniesta, and only two can play.
"Last season was the one in which he had the most minutes and played in more than 50 per cent of the matches, when he wasn't injured. But for the important games I favoured the other three.
"In the end the player went where he wanted to and I wish him all the luck in the world, he deserves it."
Vilanova also claimed that former colleague Guardiola "wasn't there for me" during his rehabilitation from cancer.
In the latest chapter of what has turned into an unseemly row between Guardiola and the club he served with such distinction as coach and player, Vilanova admitted he had been disappointed by the new Bayern Munich coach's conduct.
Vilanova underwent treatment for salivary gland cancer earlier this year in New York, where Guardiola was taking a year-long sabbatical after leaving the Nou Camp hot-seat at the end of the 2011/12 season.
Barcelona president Sandro Rosell had previously suggested Guardiola had made little attempt to visit Vilanova in the United States, claims furiously contested by Guardiola, who then claimed the club were using the issue to "cause him damage".
Rosell on Monday night attempted to diffuse the row by calling Guardiola "the best manager in the history of the club" but Vilanova himself re-opened it on Tuesday.
He said at a press conference: "People aren't interested in personal matters, but Pep got it wrong and I'm surprised by his comments.
"No-one on the board used my illness to attack him. The club tried to help me as much as possible.
"He visited me once in New York when I'd just arrived, but during my recovery from the operation... I was there for two months and I didn't see him.
"He's my friend and I needed him, but he wasn't there for me. I would have done things differently."
Vilanova disputed the suggestion the pair had fallen out after he succeeded him as Barca boss.
"I talked to him and told him what I intended to do. It was him who encouraged me to become Barca coach," he said.
"I've known him for 28 years. He's my friend. I've won titles with him and we had amazing times together."
Thiago is not the only player to leave the Nou Camp this summer with experienced duo David Villa and Eric Abidal moving to new clubs and a number of fringe players going out on loan.
Barca have been less busy brining new faces into the club, with the only major new arrival being the big-money signing of Neymar.
However, the Catalan giants are still looking to strengthen ahead of the new season and have been linked with a host of names, including Paris St Germain centre-back Thiago Silva.
Vilanova admits he is keen on the Brazil international but says he is not the only defender on their wish list.
"The intention is to bring in a centre-back. Thiago Silva is a player that we wanted to sign some years ago. I'd like to sign him, but he's not the only person we are looking at for that position."
Barca have also been linked with Roma defender Marquinhos, but Zubizarreta insisted they had not put in a bid for the 19-year-old.
Zubizarreta also confirmed Barca would not be looking to sign any more strikers despite the sale of Villa, and said they had set themselves no deadlines for completing their summer transfer dealings.
"There's no set period, up until midnight on August 31 there's time," he said.