United have failed with two offers for the Spain international and were reported to be considering a third approach in an attempt to secure a high-profile summer signing at this late stage of the window.
However, appearing in a press conference for Barca on Thursday, Fabregas said his future lies at Camp Nou.
“My dream is to play here,” he said. “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."