The Mozambique star only has a year left on his contract with Spanish side Atletico Madrid.
Per The Sun, United could secure the left-back for a fee of around 8 million.
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The Red Devils are desperate for more options in this area, as they look to strengthen their squad.
Both Luke Shaw and Tyrell Malacia have missed the vast majority of this season.
However, United face competition for Reinildo's signature from Aston Villa, who will be in the Champions League or Europa League next term.