The 22-year-old found himself on the fringes of Diego Simeone's team last term, making just 17 appearances in La Liga.
And, according to AS, Gimenez is considering his future at the club.
Gimenez is about to enter the final year of his contract but Atletico would be unable to replace him until January if they sold him this summer.
The Spanish capital club are currently under a transfer embargo, meaning they are unable to sign new players.
United and Liverpool are on the hunt for defensive reinforcements and are interested.
The Serie A giants - backed by new Chinese investors - have enquired about
Atletico are eager to keep Gimenez as they believe he is capable of replacing 31-year-old Diego Godin on a long-term basis.