United are showing an interest in the Argentine forward, and Icardi is keen on a move to Old Trafford, says TyC Sports.
However, it is understood that PSG feel Icardi is not United's top target, and the Red Devils have not made direct contact with the French champions yet.
Interest in Icardi comes amid a disastrous start to the season for United, which has seen them lose both of their top flight games against Brighton and Brentford.
Wanda Nara, the 29-year-old's agent and wife, has held preliminary talks with Galatsaray and Manchester United.
Icardi's current contract with PSG runs until the summer of 2024.