The Red Devils were keen on the Brazilian star in January, but saw a tentative enquiry for his signature rebuffed by the high-flying La Liga side.
Yet Moyes has remained interest in the 29-year-old as he plans his summer overhaul.
The Scot is set to lose Nemanja Vidic in less than six months’ time, and has made a replacement for the rugged Serbian defender a priority.
Miranda has the experience to fill the void, after helping Atletico to establish themselves as a genuine force in the Spanish top tier.
The Madrid side may be far from keen to sell, but the lure of playing at Old Trafford and being a central component of the Red Devils’ first-team may tempt the South American.
The silky centre-half is believed to be valued at around £13m.
As well as Miranda, Moyes is also watching Benfica’s Ezequiel Garay.
The Argentine has been linked with United over the course of the past few transfer windows, but a deal has never been reached.