The Belgium international is about to enter the final year of his contract in the French capital and is yet to be offered an extension.
According to RMC Sport, all three Premier League giants are eager to land the right-back as they look to strengthen their defensive ranks ahead of next season.
However, they will need to fork out £26 million to convince the Ligue 1 champions to sell.
United are in the market for a right-back with Antonio Valencia set to leave on a free transfer at the end of the campaign and 33-year-old Ashley Young approaching the twilight years of his career.
Meunier has made just 20 league appearances for PSG this season, scoring three goals, but impressed during Belgium’s run to third place at last summer’s World Cup in Russia.
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