Both clubs are said to be in the market for a new player to strengthen their backlines ahead of next season.
United splashed out a record amount for a defender last year when landing Harry Maguire from Leicester City in an £80m deal, but Ole Gunnar Solskjaer is on the lookout for someone to partner the Englishman.
City failed to replace long-serving skipper Vincent Kompany 12 months ago, meanwhile, and are looking to recruit at the back as a priority this summer.
According to The Independent, however, the Premier League pair are on a collision course as they are both eyeing up the same players.
The report indicates that City may have the advantage in the race to sign Skriniar as Inter are hoping to strike a swap deal that would involve Sergio Aguero heading the opposite way. body check tags ::