The English champions have had two bids rejected for the Spanish international, and had been mulling over a third offer.
However, Fabregas has rejected any talk of a move away from the Camp Nou, effectively ending United's pursuit of him.
"My dream has always been to play at Barca and nothing has changed," he told reporters. "I'm very, very happy here and I never thought about leaving.
"It cost me a lot to return to Barca and now I want to triumph here. I've always felt valued by the club. Everyone told me they count on me.
"It's an honour that United made two bids, but there have been no talks. I didn't talk with any club since I joined Barca two years ago."
Fabregas also refuted rumours that he used the transfer story to ask for an improved contract.