The 22-year-old has been subject to interest from Premier League rivals Liverpool too, but United are hoping to beat any competition as manager Jose Mourinho is desperate to improve his defence for the upcoming season.
The defender has one year remaining on his deal at Atletico and there have been no talks about a contract extension which means the Madrid club will want to cash in on him this summer instead of losing him for free in a year.
Gimenez will cost the Manchester club at least £30m which is worth it seeing as he is still young and will develop into a much better defender in a few years.
The Uruguay international has admitted that he is frustrated by a lack of first-team opportunities at the Spanish giants and wants more game time, which means he is open to a move.
The defender gave an interview in his home country, where he stated:
“I dream of playing in the Premier League because all matches are fairly even. I would like to go.”