The 22-year-old has fallen down the pecking order at Old Trafford, and has found game time hard to come by since the arrival of Alexis Sanchez in the summer.
Hence, the France international is believed to be considering his options, and could be set to move in the summer in search of first team football.
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The Frenchman would prove to be a perfect replacement to Eden Hazard, whose future is up in the air, as he is currently being courted by Real Madrid.
The Blues could also be looking to replace Willian, who turns 30 in August, and is also a target for Jose Mourinho.
The Red Devils and the Blues enjoy a good relationship with each other in term of transfers, with Juan Sebastian Veron swapping Old Trafford for Stamford Bridge back in 2003, and more recently, Juan Mata and Nemanja Matic swapping blue for red in 2014 and 2017 respectively.
Juventus and Tottenham Hotspur are also said to be keen on the 22-year-old, who can play anywhere across the front line. They are reportedly ready to pay around £44 million for the former Monaco man.