David Moyes's 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: “My dream is to play here. I’ve never thought about leaving. I am at the best club.
"I've not thought of anything but continuing at Barca. It cost me a lot to return and I want to be a success here.
"When an important team makes two offers for you, it's flattering, but I have never spoken to anyone from United. I haven't spoken to another club in two years."
Fabregas, 26, was reported to be keen on a return to the Premier League and United felt confident enough to mount a prolonged pursuit of the playmaker.
However, the midfielder says he never entertained thoughts of leaving Camp Nou, where he has won the Copa del Rey and one Liga title since joining the club in 2011.
"Things have been made up," the former Arsenal captain added. "I have had messages from (president Sandro) Rosell, (vice-president Josep Maria) Bartomeu, and (former coach) Tito (Vilanova). I have spoken with Tata (new boss Gerardo Martino).
"I have felt wanted at all times. I have never had a problem. And it isn't true that I have asked for a new contract either.
"I was always relaxed. I did not have to clear up anything because in my head I was only going to stay at Barca."
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.