Sky Sports News television, the BBC and the domestic Press Association news agency all said that the English Premier League champions were interested in signing the Spanish international.
The Press Association said that an offer had been submitted for the player, who came through Barcelona’s youth academy before joining Arsenal as a 16-year-old in 2003.
Sky Sports News, however, said a potential stumbling block could be a clause in Fabregas’ contract that Arsenal have first refusal should he decide to leave the Camp Nou.
Barcelona said they had no comment to make when contacted by AFP.
If completed the Fabregas move would represent new manager David Moyes’ first major signing since the former Everton boss succeeded Alex Ferguson during the close season.
United, who are currently on a pre-season tour of Asia, have the cash to allow Moyes to chase “a stellar player” before the start of the upcoming season, the club’s chief executive Ed Woodward was quoted as telling British media on Sunday.
According to Woodward, the Old Trafford club are “absolutely” able to compete for players in the £60 million to £70million bracket.
News of a potential offer for Fabregas emerged a day after confirmation that Barcelona had sold Spain Under-21 captain Thiago Alcantara to European champions Bayern Munich.
Fabregas graduated to become the Gunners’ captain and one of their most influential players before returning to Barca in a £25.4 million, five-year deal in August 2011.
Since then he has helped the Catalan giants claim the Copa del Rey in 2011-2012 and La Liga in 2012-13.