The Spain international is enjoying himself back at the Nou Camp, where he began his career, and does not want to head back to England just two years after leaving Arsenal.
United have failed with two bids for Fabregas this summer and there has been speculation that the Premier League champions will go back in with a third and final offer before the transfer window closes.
There were also reports suggesting that Fabregas would be interested in a move to Old Trafford, if a bid was accepted, but he is adamant he does not want to leave.
"I have never said that I could go, nor have I talked to the president or the coach about it," he told TVE show Esport Club.
"What I don't know is how this can be said to be true just because some journalist wrote it on Twitter.
"My dream is to stay here and succeed."
Fabregas' aim now is to impress new Barcelona coach Tata Martino and win a regular place in the Argentinian's plans for the season.
He added: "I have a great desire to achieve even more and I am committed to this club and proud to be here."
The former Arsenal captain has started Barcelona's opening two games of the new season which have brought wins against Levante and Malaga in La Liga.