Depay is the Eredivisie’s leading goalscorer and scored in the 4-1 win over Heerenveen on Saturday as Phillip Cocu’s men sealed the league title for the first time in seven seasons.
Liverpool and Tottenham have been linked with the 21-year-old, but PSV technical director Marcel Brands has revealed United have made an intitial approach.
"We have had a telephone call from them about him," Brands said on Dutch television.
"But no talks have been held yet. There are several top clubs who have expressed an interest."
Brands added Depay, who has scored 20 league goals this season, would cost more than the £14.5m Premier League side Tottenham Hotspur reportedly bid for the striker.
"It will be much higher than the offer from Tottenham Hotspur," Brands added. "He will be very expensive."
Cocu said he expects Depay, who played in last year's World Cup in Brazil, to leave in the summer, along with fellow Dutch international midfielder Georginio Wijnaldum.
"The chance is really good that they'll both go," Cocu said. "But I do hope we'll be able to keep the rest of the team. A few mutations are not so bad but there must not be too many."
The goal meant the Argentine was the first player to reach 20 Premier League goals this season.
Aguero had several chances to add to his tally, with one effort saved by the sprawling Adrian following an incisive move from Pellegrini's side.
West Ham had a late Kevin Nolan shot saved by Joe Hart, but they rarely threatened a comeback.
West Ham boss Sam Allardyce:
"The two goals we gifted them are pretty disappointing on the basis of how we conceded them.
"You can't make the mistakes we made and expect to get anything out of a game at Manchester City. We created our two best chances late on but can't seem to be as clinical as we used to be.
"The goal threat from us has not been as potent as we showed earlier on in the season."
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