Manchester City and Chelsea are reportedly two of those clubs who 'desire' the 26-year-old centre-back.
While the latter have maintained their interest for several months, Pep Guardiola's Manchester City have allegedly had a €80 million bid rejected in the past - which is believed to be during the last summer transfer window, when the club ultimately decided to sign Ruben Dias from Benfica.
Atlético signed the Uruguay international from Danubio Futbol Club in 2013 and he has steadily become a mainstay in the La Liga side, making 21 appearances for them so far this season.
It is said that the player is content with his life in Madrid, and has no plans to 'abandon' his current team as they battle to become La Liga champions for the eleventh time in the club's history.
Centre-back is a position that Manchester City have invested in heavily over the past few years, recently signing Ruben Dias from Benfica for a reported £61 million, and Nathan Aké from Bournemouth for another £41 million.
While Aké has spent much of the season injured, Dias has had a transformative effect on the Manchester City defence, partnering well with both Aymeric Laporte and the resurgent John Stones.
While this seems to be a position Pep Guardiola's team are currently blessed in, it is believed that they will lose Spanish international Eric Garcia when his contract expires at the end of this season. The young defender is edging closer to a dream move to Barcelona.
This could subsequently create a space to be filled by the likes of Giménez, though he is supposedly worth upwards of £70 million, and feels valued at the Metropolitano.
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