Sky TV sources understand United's opening bid of £25million, communicated to Barcelona on Monday, has sharpened interest from Arsenal, Chelsea and Manchester City.
And Arsenal must now decide whether to follow up their initial interest and take advantage of a clause in Fabregas' contract allowing them first refusal on their former captain, who rejoined Barca in 2011 following eight years in north London.
For his part, Fabregas has repeatedly said he is happy in Catalonia, and that stance was reiterated by Barca boss Tito Vilanova on Tuesday.
Vilanova said: "It's normal to receive offers for our players from other teams. We have very good players, and we have to be very happy to have Cesc with us.
"I am conscious that he has received offers for other teams, but I had a conversation with him and he let me know that we wanted to stay here, and his dream is to be successful here.
"So he is not thinking about any other club, not even for money or for minutes, even if he knows all the competition he has here with Xavi, Iniesta and also this year against Sergi and Roberto, but he told me that his dream is to be here. I'm not worried at all."
Source: Manchester City MAD