Tottenham Hotspur are also said to be keen on the Pole.
At the end of March it was reported by The Sun that Tottenham Hotspur were ready to snap up the Polish international centre-back Kamil Glik in a deal believed to be worth around £8 million. The Torino defender has impressed this season and Spurs need new centre back options after a difficult season at the back.
However, they are not the only Premier League team interested.
Glik has a contract at Torino until the summer of 2017, so he is certain to cost a fair amount.
He has previously intimated he will stay in Turin, but it remains to be seen whether any Manchester United interest could change his tune.
Torino's president Urbano Cairo also made it clear that none of his players were unavailable, at the right price.
But both Spurs and Manchester United now have another rival - as Manchester City are said to be closing in on a deal.
As reported by Forza Italian Football, City have apparently began to track the player after an excellent season at City.
City need a new centre-back, with Martin Demichelis ageing, Vincent Kompany's fitness in doubt and Eliaquim Mangala failing to impress.
Glik might just be the man for the job.