United boss David Moyes has admitted signing a new midfielder is his priority ahead of the new season, although the Spanish club have warned the Premier League champions off the former Arsenal man, who rejoined Barca in 2011 following eight years in north London.
Barcelona vice president Josep Maria Bartomeu was quoted by Spanish daily Sport on Friday: "Barcelona can assure you we will not entertain any offers for Cesc. It is totally ruled out, he's not for sale."
However, having failed with a bid of around £25m last week, United have returned with an improved offer in a bid to land Moyes his first big signing since joining the club.
Chief executive Ed Woodward left United's pre-season tour ahead of schedule on Wednesday in order to return to Europe to carry out urgent transfer business, with it understood to concern a player arriving at Old Trafford.
And goalkeeper David de Gea has said he would welcome Fabregas at Old Trafford, telling the Daily Mail: "He is a great player, very skilful, knows how to win things and you always want those type of players in your team."
Robin van Persie has also expressed his desire to be reunited with Fabregas, having played alongside the midfielder for Arsenal.
Asked after United's 5-1 pre-season victory over the A-League Al Stars whether he would welcome Fabregas, Van Persie said in Sydney: "Of course, he's a great player."
Moyes was also questioned on possible new recruits after the clash in Australia, but insisted there had been no developments over the past 24 hours.
"I've not had any more news since we last spoke yesterday," said Moyes. "I have no more updates so I couldn't give you anything positive or negative."