The 21-year-old is tipped for a big future by many in Spain and already has over 20 caps for Uruguay.
Real Madrid have been linked with a sensational £51m bid this summer and Paris Saint-Germain have scouted the centre-back too.
But, according to Marca, both Chelsea and City are also very interested in trying to land Gimenez this summer.
The Premier League pair are both in need of defensive reinforcements at the end of the season and have earmarked the Uruguayan as a target.
Atletico, however, are reluctant to sell and are likely to rebuff any approaches.