The Red Devils are allegedly considering bringing a new centre-back to the club ahead of the 2020-21 campaign despite signing Harry Maguire in a world-record deal last summer.
Skriniar has long been linked with a move away from San Siro, with Manchester City believed to be admirers of the 25-year-old, who still has three years left to run on his contract with Antonio Conte's side.
However, according to Tuttosport, United have made a €65m (£58m) offer for the Slovakia international as the English giants bid to bring him to the Premier League during this summer's transfer window.
The report claims that Inter wanted €80m (£71.6m) last year but are no longer in a position to ask for that amount due to the state of the market.
Skriniar has made 36 appearances for his Italian club during the current season, although he has only been involved in one of their last four Serie A matches due to suspension. body check tags ::