The Telegraph says Pogba's agent Mino Raiola is discussing personal terms with PSG, who believe they can sign the midfielder for less than half the £89million he cost United in 2016.
Pogba has less than 12 months left on his £290,000-a-week contract and has given no indication that he is interested in signing fresh terms at Old Trafford.
United anticipate the Ligue 1 giants will make their move for the France international before the transfer period ends next month, believing they can snare him away for £43m.
United paid what remains a Premier League record to sign the 28-year-old from Juventus five years ago, but now face losing him on a free next summer if they do not sell between now and August 31.
The Frenchman shone at Euro 2020 but is due to return for pre-season training next week after going on a family holiday in Florida following his country's exit at the hands of Switzerland.
Asked about the situation last month, he said: "I have one year left on my contract, everyone knows that. There have been no concrete proposals for extensions. I'm still in Manchester."
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