According to the Telegraph, the Brazilian defender is entering the final-year of his contract and the Spanish capital club are concerned that they will be forced to sell him this summer rather than lose him on a free at the end of next season.
Jose Mourinho has admitted that he is looking to bring in one or two more players in the summer and it is believed that the manager is keen to sign a defender in the summer.
Real Madrid's Raphael Varane is said to be the Portuguese manager's primary target, but his current employers are reluctant to let him leave and the player himself has indicated that he would like to remain with the 10-time European champions.
This has prompted the Blues to target Miranda, who will be available for a relatively lower fee due to his contract situation. But with John Terry and Gary Cahill having stellar seasons, it remains to be seen if the Brazilian will be given a starting role in case he signs for the Stamford Bridge outfit.
On the other hand, United could give him a starting role at the heart of their defence pairing him with either Chris Smalling or Phil Jones, as Louis van Gaal has made signing a central defender a priority in the summer.
The Red Devils were heavily linked with Borussia Dortmund's Mats Hummels, but after his rejection, they turned to the Atletico star, who was close to completing a move to Old Trafford last summer, only to see it collapse due to the Spanish club's hefty demands.
Meanwhile, Chelsea could still hold the advantage when it comes to signing Miranda as Atletico are keen on taking left-back Luis Felipe back to Vicente Calderon, after the Brazilian's failed spell in the Premier League since joining Mourinho's side last summer.