Sources close to United have informed BBC Sport of a third bid for the Catalan, this coming a few hours after Andoni Zubizarreta, Barcelona sporting director, said the Red Devils have abandoned their interest.
United, who have yet to make a major signing since David Moyes succeded Alex Ferguson as manager, have already had two bids for the Spanish international rejected by Primera Liga champions.
"Manchester United were interested in the player, but they have also understood our stance that we don't want to sell him," the former Spain goalkeeper was quoted as saying by Barcelona based daily Sport.
"They have given up on signing him."
Despite claiming the first league title of his career last season, Fabregas has endured a largely frustrating time in the two years since he returned to the club he left as a 16 year old to join Arsenal.
His opportunities in Barca's midfield have been limited by the presence of international teammates Xavi, Andres Iniesta and Sergio Busquets, while his role lying behind the main striker is occupied by four-time world player of the year Lionel Messi.
However, with the sale of Thiago Alcantara to Bayern Munich and the 33-year-old Xavi expected to play fewer games this season, Zubizarreta insisted Fabregas will be a key part of the squad.
"Cesc is an extraordinary player, we are counting on him. He has vision, he helps in defence, he is our number four and we are not going to sell him."
Fabregas scored twice on his first appearance of the season for the Catalans in their 8-0 hammering of Santos on Friday and has travelled with the squad to take part in coaching clinics in Palestine and Israel before they embark on a tour of Asia.
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