David Moyes' side had two bids for the former Arsenal man rejected by Barcelona earlier this summer, while Nou Camp sporting director Andoni Zubizarreta declared at the start of the week that United had given up on trying to sign the Spain international.
Fabregas ruled out a move away from Barcelona while at the Confederations Cup in June but kept silent after United made their interest in him official, prompting speculation that he was in favour of a transfer.
But speaking in a press conference in Malaysia, the midfielder said: "Triumphing in Barcelona is what I have been hoping for all my life, it's been my dream since I was a child.
"I am very happy at Barcelona and I haven't spoken to any other club in the last two years."
Fabregas also defended not making a statement on his future in the midst of speculation about United's interest.
"I've been relaxed about it the whole time, I didn't have to clarify anything because the only thing I was thinking about was staying at Barca," he said.
"I haven't deceived anyone or hidden anything, I told the club's press department that I would speak when it was my turn to speak to the press."
United responded on Wednesday afternoon when a spokesman said: "We appreciate Cesc is a contracted player at Barcelona and completely respect everything Cesc has said today."
Fabregas returned to his boyhood club from Arsenal in 2011 and helped Barcelona win last season's league title as well as the previous year's Spanish cup.