Sky Sport Italia is reporting that both the Blues and Juventus are keen on a move to sign the 27-year-old from the Spanish club this summer.
The former Manchester City man has spent three seasons with Atletico Madrid since joining the La Liga club from Fiorentina back in 2015.
The 27-year-old Montenegro international made 36 appearances for the Spanish side last season but it is being claimed that he could be on his way out of Atletico Madrid this summer.
Chelsea FC and Juventus are both said to be keen on signing the defender as they look to bolster their squads ahead of next season.
The west London side are believed to be on the lookout for a number of new signings this summer as they look to assemble a team capable of challenging for the Premier League title next season.
The Blues ended up in a disappointing fifth place in the Premier League table last season as they missed out on qualification for the Champions League.
However, they did end the campaign on a high by beating Manchester United in the FA Cup final back in May.
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