Manchester United have denied triggering Atlético Madrid defender Miranda's £24 million release clause.
The 29-year-old was instrumental in Atlético's first La Liga title win since 1996 and played the full 120 minutes of their Champions League final defeat to Real Madrid on Saturday.
Spanish sports daily AS claimed the Brazilian, controversially not selected for the Seleção's World Cup squad, had been offered a four-year contract by United, however the club have denied the report.
Centre-backs Nemanja Vidić and Rio Ferdinand are leaving United this summer after their contracts were not extended.
New coach Louis van Gaal is eager to bring Borussia Dortmund defender Mats Hummels to Old Trafford, however Miranda has shone under Diego Simeone at Atlético.
He joined the Rojiblancos from São Paulo in 2011 and has become an integral part of the side. Miranda started in the 2012 Europa League final rout against Athletic Bilbao and nodded in the winner at Real Madrid in last year's Copa del Rey final.