The Red Devils have endured a quiet summer on the transfer front, with Uruguayan youngster Guillermo Varela the only arrival.
Moyes is keen to add at least one big name player to his squad, and is believed to be keen to bring in a new centre-back.
Miranda fits the bill on both fronts, and United are hopeful that they can convince him to swap the Vicente Calderon for Old Trafford.
The 26-year-old is thought of as one of La Liga’s finest defenders, and was a key part of Atletico’s Copa del Rey winning side of last season.
Despite his importance with the first-team, the Spaniards are believed to be willing to sell for around £6m, a price that United more than happy to match.
Miranda is also able to play at right-back and in central midfield, which is thought to be seen as useful by Moyes.
Meanwhile, the Premier League champions are also keen to agree deals for Everton’s Marouane Fellaini and Leighton Baines.
Moyes has already seen multiple moves for the duo knocked back by his former club.
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