United are said to be keen to find a buyer and hope that his age, and the fact he was one of the most promising defenders when he joined, will see offers come in.
Shaw has struggled to make an impression in Manchester as he has never lived up to the hype surrounding him.
The Belgian midfielder is a key asset for Jose Mourinho, and if United don't sort out the scenario, then the Portuguese is likely to get really upset.
He has also not given up on his chances of making the England national team, which will play in the World Cup in Russian Federation next year.
Leeds United legend Johnny Giles believes Manchester United boss Jose Mourinho wants a move to PSG. £20 million represents a good deal for a player of Shaw's quality, as top quality left backs are a rarity right now.
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The 54-year-old is halfway through a three-year deal at Old Trafford, though the club have the option of triggering a 12-month extension.
Everton are also looking at signing him as a statement of intent about their own ambitions and also as a long-term replacement for Leighton Baines.
Shaw's career began to stumble after his horror leg break against PSV Eindhoven back in 2015.
Shaw is a classy left back that is known for his defensive prowess as well as marauding runs further up the pitch.
After a second consecutive summer of colossal spending, Mourinho has been informed he must sell before he can buy in January and Shaw, who has made just two first-team appearances this season, has emerged as a prime candidate to be cut loose in order to raise funds.