Sky 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."
Sky sources are indicating, though, that Fabregas would be prepared to move if Barca accepted a bid.
That has not happened yet, and United are still awaiting a response to their offer, which was lodged as David Moyes steps up his chase for a creative influence.
The Spanish champions, meanwhile, may be reluctant to lose another midfielder so soon after Thiago Alcantara's recent move to Bayern Munich.
Speaking last month, Fabregas confirmed he is happy at Barcelona and dismissed talk of his departure by reiterating his desire to stay at the Camp Nou.
"I've always said that I'm happy at Barca. Whoever says that I'm leaving doesn't know me and has never spoken with me," said the 26-year-old.
"Nor with my agent, because he knows that I don't want him to talk with other people about me. I'm very private and I don't even talk about these things with my family.
"If someone says anything that isn't that I want to play at Barca, it's completely absurd."
New United manager Moyes is still waiting to make his first signing after missing out on Thiago.
However, Moyes says he has money to spend this summer and that the Red Devils are looking to land 'the best players' around.
After seeing his first game at the United helm end in a 1-0 defeat to the Singha All Star XI on Saturday, Moyes said: "Isn't it great that the club says, 'There's no budget here, you go get who you want to get, just go and do it'.
"We are looking at the best players. I do think it's important that we show people we are carrying on the traditions and trying to take the club forward.
"I will not name anybody, but certainly we are always looking at the best players. I think we are trying to strengthen in a couple of areas. We are short in midfield.
"We are also a club which tends to invest in the youth side, so you can expect us to go for players in that age group.
"We are working hard to make sure the first signing is the right one. I have been left a really good team and I want to add to it sensibly."