Gunners boss Arsene Wenger has made no move to re-sign Fabregas, but United's interest looks to have brought rivals City and Chelsea into the race for his signature.
And sources in England have revealed the 26-year-old would be open to a move back to the Premier League, who joined the Nou Camp giants two years ago.
Barcelona look unlikely to accept the opening offer from the Old Trafford outfit, paving the way for some of the other top-four clubs to try and hijack any potential deal.
David Moyes is said to be eager to inject a more creative influence into the side he inherited from Sir Alex Ferguson.“He wants to succeed here”Barcelona head coach Tito Vilanova
United are now thought to be waiting a response from Barca, having put forward their surprise offer on Monday.
The La Liga giants head coach Tito Vilanova revealed his views on recent interest in his player, telling the Spanish media: "I'm aware there have been offers.
"I had a conversation with him and he told me that he wanted to continue here and that he didn't want to go to another big club.
"He wants to succeed here."
The Champions League winners nipped in and agreed a deal to bring the playmaker to Germany, where he'll link up with ex-boss Pep Guardiola, who is embarking on his first season at the Bayern helm.
A fee of £21.6m has been agreed between the two clubs, as well as a commitment to hold a friendly by 2017.