Sources told ESPN that United are now in the process of applying for his Governing Body Exemption with the English Football Association.
United completed a deal worth an initial €21 million for Diallo on the final day of the summer transfer window in October, but were unable to fly the 18-year-old to Manchester due the Ivory Coast-born player's ongoing wait for an Italian passport.
- Festive fixtures will reveal if Man United are for real
- Ogden: Man United should swap Pogba for Ronaldo
- Stream ESPN FC Daily on ESPN+ (U.S. only)
- Insider Notebook: Juventus propose Pogba-Dybala swap deal
Sources told ESPN that the passport issue has now been resolved, with Diallo being granted his Italian documents earlier this month.
But he is yet to receive clearance to play in England and is still waiting for United's request for a work permit to be cleared by the UK government.
Sources said, however, that United have been given positive indications that Diallo will be given the necessary paperwork in the coming weeks.
The Abidjan-born youngster has made just two first-team appearances for Atalanta this season -- both coming from the substitutes' bench -- but he is regarded as one of the most exciting emerging talents in Europe.
And there is a confidence at Old Trafford that, once Diallo is cleared to play in England, he will be able to link up with Solskjaer's first-team squad for the remainder of this season.