Gimenez has lost his place in Diego Simeone's starting XI recent months.
He was left on the bench as Atletico salvaged a 1-1 draw with fierce rivals Real Madrid last week.
The 22-year-old is one of La Liga's rising stars and his stock has seen him linked with a move to the Premier League.
Jose Gimenez has lost his place in Diego Simeone's starting XI Five most likely summer deals according to the bookies Wed, February 1, 2017
Express Sport takes a look at the five most likely deals that could happen this summer. Odds provided by BetStars
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Jose Mourinho wants to bring him to Old Trafford with Chris Smalling and Phil Jones currently out for the long-term.
He was heavily linked with a move for Benfica's Victor Lindelof in January but Giminez now appears to be his preferred target.
Jose Mourinho and Jurgen Klopp could have a transfer scrap this summer
However, Liverpool boss Jurgen Klopp is also an admirer.
Both clubs will have to fork out £33million to land him.
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While Atletico will look to keep him, Gimenez may quit the Vincente Calderon in order to secure first-team football elsewhere.