Earlier this week, it was claimed that Lyon were the only club interested in the out-of-favour 22-year-old, while Jose Mourinho revealed on Friday that United had received no bids which came close to meeting their valuation.
However, according to The Sun, PSG are considering a bid for the player, who has made just one appearance for United since the start of November.
It has been suggested that PSG's sporting director Patrick Kluivert is keen to capitalise on the availability of his countryman, who he believes can still fulfil his potential with regular first-team football.
United are unlikely to entertain any offers short of £15m, but PSG may decide to test the water should they look to follow up their interest in the former PSV Eindhoven player.
Depay has made just 16 Premier League starts since joining United in June 2015, with a further 17 outings coming from the bench.