The Red Devils have already paid big to land Ander Herrera and Luke Shaw this summer, but Louis van Gaal’s overhaul of his squad is not likely to end there.
The Dutchman is rumoured to have £200m to spend, and is ready to take his transfer splurge past the £100m mark in the coming weeks.
The pair, who are currently away the World Cup, are seen as LVG’s top targets in the two roles he is keen to address.
Hummels is a natural replacement for Nemanja Vidic at centre-back, with the German one of the few genuine world-class defenders on the planet.
Dortmund are reluctant to sell, but United the player himself is thought to be open to a switch to Old Trafford after watching a number of stars leave BVB in recent seasons.
Di Maria is said to have impressed van Gaal in Brazil, and could be used as the man to spark the club’s attack and get the best from Wayne Rooney and Robin van Persie.
Despite his fine displays or club and country, Real Madrid are understood to be ready to sell for close to £45m. Hummels will cost around £30m.