He has just 12 months remaining on his current contract and a £39.5 million release clause in his current deal.
Interest has been reported from Old Trafford and Anfield in the recent past, while Arsenal were said to be contemplating a move in the summer of 2016.
Gimenez told Uruguayan journalist Federico Buysan on his ambitions: "I dream of playing in the Premier League because all of the matches are fairly even.
"But if Atletico offer me a contract for life, I will stay."
It remains to be seen what Atletico’s plans for Gimenez are, having restricted him to just 12 La Liga starts in the 2016-17 campaign.
He has been with the club since 2013, but has rarely been a regular on the team sheet.
Despite that, the 22-year-old is grateful for the opportunities he has been given and for a platform on which to prove himself to other potential suitors.
He added: "Atletico taught me a lot from the first day I arrived.
"I am privileged to be at the club."
Pressed further on his future, with Serie A heavyweights Inter also reported to be in the mix, Gimenez said: “I am relaxed about the rumours about my future and I always speak with my representatives.”
Gimenez has seen United already add Victor Lindelof to their ranks this summer, but Liverpool remain in the market for a new centre-half and Inter are expected to be busy with another refresh of their squad at the San Siro.