The 17-year-old striker has caught Fergie's eye despite making just six first-team appearances, says The Sun.
Argentine Villalva has scored two goals in his brief professional career and has already represented his country at Under-17 level.
Nicknamed 'Keko', Villalva is refusing to get carried away with the Red Devils' interest in him.
He said: "I am calm about my future and will not let things go to my head about a move to Europe.
"I'm happy to continue playing at River Plate and want to help them become champions."