The Mirror says Fabregas will consider a switch to United if Barca accept a bid for him and is now waiting to see what develops.
A second offer of £30 million - rising to £35 million in bonuses - was tabled by United over the weekend.
If United can find a breakthrough, they will tell Fabregas he can double his £100,000-a-week Barca wages by moving to Manchester this summer.
A Spanish source said: “Manchester United are deadly serious about signing Fabregas and have made a second bid.
“There is a lot of uncertainty at Barcelona at the moment and it is hard to predict what will happen.
“But one thing is for sure and that is that Fabregas could earn a lot more money by joining United.
“That will not be his top priority, but United hope it will help them to clinch a deal.
“Cesc had been planning to stay in Barcelona for at least one more year, but if the club accept a bid for him, then, of course, he will have to think about his future.”