Jurgen Klopp is a long-term admirer of the 29-year-old central midfielder and is ready to attempt to lure him to Anfield this summer.
But he faces real competition from Jose Mourinho, who worked with the £30million-rated star at Stamford Bridge.
Fabregas has two years left on his £170,000-a-week deal but he’s only started 10 Premier League games this season and is now edging towards a Chelsea exit, according to the Express.
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Italian giants AC Milan and Inter Milan are keen but Fabregas is thought to prefer to stay in England.
Chelsea are also thought to be open to selling him as they edge closer to landing Tiemoue Bakayoko from Monaco to partner N’Golo Kante in midfield in 2017/18.
Fabregas will wait until the end of the season before he makes any decision on his future, with both Liverpool and United waiting in the wings to sign him.