The Red Devils revealed on transfer deadline day in October that they had agreed a move for the 18-year-old, but the switch depended on Diallo receiving a work permit.
Diallo was born in the Ivory Coast before moving to Italy at a young age, and a recent report claimed that United had still not finalised a deal for the attacker.
However, Solskjaer is hopeful that the move will be signed off in the early stages of 2021.
"Amad has come on a few times for Atalanta lately, he is a very exciting young boy and talent and hopefully we'll get the work permit and he'll be with us in January. A very, very exciting boy as well," Solskjaer told reporters.
Diallo has made two first-team appearances for his Italian club during the 2020-21 campaign, including 22 minutes against FC Midtjylland in the Champions League at the start of December.
The right-sided forward has scored once in five outings for Atalanta in all competitions. body check tags ::