The Brazilian star has established himself as one of the best midfielders in Serie A. He is expected to leave Atalanta at the end of the season.
United have been long-term admirers of the 25-year-old and they were keen on landing him last summer before the purchase of Manuel Ugarte.
The Red Devils are prepared to make a renewed approach later this year and they could be willing to pay around €60 million for his services.
However, United are set to face stiff competition from arch-rivals Liverpool, who currently lack quality depth in the defensive midfield role.
Ryan Gravenberch has been ever-present as the no.6. Wataru Endo is the back-up option, but he is expected to be offloaded this summer.
Ederson would provide strong competition for places for Gravenberch. He would do the same with Manuel Ugarte at the Red Devils.