Website TEAMtalk is reporting that the Red Devils and the Merseyside outfit are alongside the likes of Manchester City, Arsenal and Chelsea FC in sharing an interest in the 24-year-old defender.
According to the same story, Liverpool FC and Manchester United are among the clubs who had scouts watch the Slovakia international when his side took on Wales on Sunday night.
Skriniar played the full 90 minutes as Wales ended up claiming a 1-0 victory over Slovakia in their Euro 2020 qualifier in Cardiff.
Skriniar has long been touted as a target for Premier League clubs and he has been in solid form for Inter Milan so far this season, making one assist in 25 Serie A appearances.
Both Liverpool FC and Manchester United are likely to be linked with a number of players in the coming weeks and months as they look to strengthen their squads this summer ahead of next season.
Liverpool FC will return to Premier League action on Sunday when they welcome Tottenham Hotspur to Anfield as they look to keep their place at the top of the table.
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