Skriniar, 23, only joined Inter from Sampdoria in 2017, with the Slovakian signing a five-year contract at San Siro.
Last term, the centre-back made 40 appearances in all competitions - scoring four times in the process.
According to La Gazzetta dello Sport, United offered Inter £57m for the defender, but the bid was quickly turned down, with Inter considering him untouchable.
The Red Devils have been strongly linked with a move for a new centre-back this summer, and it is understood that the club are considering dropping their interest in Tottenham Hotspur's Toby Alderweireld.
United will return to pre-season training next month ahead of their trip to the United States.