Diallo, 18, has only played 25 minutes for Atalanta in Serie A but United are keen to sign the young winger for a fee worth €21 million, plus another €20m in add-ons, sources have told ESPN.
The deal will have to wait until January to be completed due to work permit regulations, sources added.
United have long been looking to bolster their resources on the wing. Sources told ESPN Diallo will be considered a first-team signing, along with 18-year-old Facundo Pellistri who was signed from Uruguayan side Penarol on Monday.
Diallo was close to signing for Parma earlier in the summer, but the deal broke down.