The 29-year-old centre-half played in the Champions League final extra time defeat against city rivals Real in Lisbon on Saturday.
Miranda was a mainstay for Diego Simeone’s La Liga champions last season and is set to link-up with Louis van Gaal at Old Trafford after being offered a four-year deal.
Clauses are mandatory for all players in Spain, and with United seemingly operating with a blank chequebook this summer, the hefty fee hasn’t deterred them.
Brazil coach Luiz Felipe Scolari didn’t pick the big defender in his World Cup squad – a decision that has come as a surprise given Miranda’s recent performances.
Spanish newspaper AS claim that he has been in Manchester looking at schools in the area ahead of a potential deal.
Van Gaal has identified the heart of his defence as a problem area, particularly after the departures of Rio Ferdinand and Nemanja Vidic has left the squad devoid of numbers.
And Miranda, despite his age, appears a safe choice after enjoying a renaissance on the continent since moving to Vicente Calderon three years ago.
He did move back to Brazil with Sao Paulo in 2006 after ill-fated one-season spells with Coritiba and Sochaux.
United have also continued to keep tabs on Paris Saint-Germain’s Adrien Rabiot, who wants to leave the club over a lack of games.
The 19-year-old is highly thought of in France and is the source of interest from Premier League clubs including Manchester City, Arsenal and Chelsea.