The former-Arsenal captain has been linked with a return to the Premier League.
United and Arsenal are thought to be keen, with the Old Trafford club reportedly eying a fruitful partnership with ex-Emirates Stadium teammate Robin Van Persie.
But the 25-year-old central midfielder has confirmed he's not received a single offer, and that he wants to succeed at the Nou Camp anyway.
Speaking to Movistar, Fabregas said: "People talk a lot but the truth is that no-one has spoken with me.
"I want to triumph in Barcelona, that club is my home and I always dreamed of playing there, so I will try and succeed there as long as I can."
New United boss David Moyes has been tipped to dip into the transfer market for a central midfielder, and Fabregas is one of the world's best.
But the Spain international is confident of establishing himself at Barcelona, and looking forward to playing alongside new signing Neymar next season.
"Neymar will need time to adapt because he is coming from a completely different type of football from what he will find here," continued Fabregas.
"We need to help him settle in and grow so that he can give us great nights."
United are short of central midfield options, with Paul Scholes now retired and Darren Fletcher a long-term absentee. Michael Carrick, Anderson and Tom Cleverley are current first-choice midfielders at Old Trafford.