Previous reports have suggested that the Red Devils have offered almost £25 million for the 29-year-old, who was a key part in Atletico's title-winning team last time round. He made 32 league appearances for Diego Simeone's side and popped up with two goals during the course of the season.
Manchester United interest
In recent weeks it has been suggested that a deal to take the defender to Old Trafford could be close - and that is something confirmed in the Spanish press today.
The Mirror, citing Spanish paper AS as a source, report that the transfer is 'almost complete' - although there is no mention of price.
The news will come as a blow to Atletico, who are struggling to keep together the team that made it to the Champions League final. The likes of Diego Costa, Filipe Luis and Tiago are expected to follow Miranda out of the door, while Thibaut Courtois will end his three-year association with the club and return to Chelsea.
Manchester United look short of options at the back and are expected to resolve that issue this summer.
Both Nemanja Vidic and Rio Ferdinand have left Old Trafford, leaving Phil Jones and Jonny Evans as the club's most likely defensive pairing as it stands.
However new boss Louis van Gaal, who will arrive at Manchester United after the World Cup, is unlikely to be content to rely on those two, and appears to have targeted a move for Miranda.