The Blues are said to be looking for a replacement for David Luiz, who joined Paris Saint-Germain earlier this summer for a fee of around £50million.
Miranda played a key part in Atleti's La Liga triumph last season, making 32 appearances as he established a partnership alongside Diego Godin that became recognised as one of the finest in Europe.
The Brazilian also played a large part in helping Los Rojiblancos to a Champions League runners-up finish, and Blues boss Jose Mourinho is said to be keen to recruit Miranda, according to Spanish publication Marca.
Chelsea have already raided the Vicente Calderon for Diego Costa and FIlipe Luis this summer, for around £47 million, and the pair are represented by Portuguese agent Jorge Mendes, who also looks after Miranda's interests.
However, do the Blues really need to splurge on a new centre-back?
John Terry signed a new contract earlier this summer, and the Chelsea captain was one of the standout defenders in the Premier League last season, as he made 34 appearances, alongside England international Gary Cahill.
Tomas Kalas also showed that there is strength in depth in the club's defensive ranks, with the young Czech making two appearances, which included snuffing out Luis Suarez and co. as the Blues beat Liverpool 2-0 at Anfield in April.
Kalas will spend the season on loan with Bundesliga side FC Koln, but Luiz's departure has facilitated the call up for young Frenchman Kurt Zouma.
The highly-rated 19-year-old was signed from Saint-Etienne back in January for around £12million and has featured in the Blues' pre-season friendlies.
Powerful, quick and good on the ball, it is easy to see why Chelsea were so keen to land the talented youngster earlier this year.
The dependable Branislav Ivanovic also offers cover as a centre-back, should Mourinho need it next term, which leads us to ask if Chelsea really need to strengthen their defensive ranks this summer?