The 22-year-old was heavily linked with Barcelona last summer but ended up joining Atletico from Villarreal on a five-year deal.
United are in the market for a new central midfielder this summer with Ander Herrera reportedly set to leave the club to join Paris Saint-Germain.
And according to Marca, United are in the race to sign Rodrigo as a replacement and are willing to pay the midfielders €70 million (£60m) release clause.
But the report also claims that United face competition from Manchester City, Bayern Munich and PSG.
City reportedly view Rodrigo as a potential long-term successor to Fernandinho, who turns 34 in May.
Rodrigo, who has been capped five times by Spain, plays at the heart of Atleticos midfield and has been likened to Barcelonas Sergio Busquets.
Earlier this season, Barcelona legend Xavi admitted that his former club should have beaten Atletico in the race to signRead More – Source