The Uruguay international left his homeland in 2013 when he joined Los Colchoneros from Danubio, but has struggled to establish himself at Vicente Calderon.
Gimenez started just 12 games in La Liga last term, although he helped Diego Simeone's side reach the Champions League final, where he featured from the start as they lost to fierce city rivals Real Madrid for the second time in four years.
The 22-year-old centre-back was previously linked with a move to Arsenal last year, while Liverpool and Manchester United have been credited with an interest in recent weeks.
Gimenez insists he would not think twice about signing a contract extension at Atletico, with his current deal expiring in June 2018, although he does harbour ambitions of testing himself in the top tier of English football.
"I dream of playing in the Premier League because all of the matches are fairly even," he conceded to Uruguayan journalist Federico Buysan in an interview.
"But if Atletico offer me a contract for life, I will stay. Atletico taught me a lot from the first day I arrived. I am privileged to be at the club.
"I am relaxed about the rumours about my future and I always speak with my representatives."