United snapped up the 18-year-old in a £37million deal in October but he remained with the Serie A club for the opening months of the season.
Reports from Italy this week claimed Atalanta had been turned down in their bid to keep him on loan for the second half of the campaign, with the player said to be close to receiving the paperwork he needs to move to England.
Gasperini told Corriere dello Sport the player would "clearly" move to Old Trafford after the issues around the move had been resolved.
"There seemed to be transfer difficulties but as soon as they are unlocked the player clearly goes to Manchester United," he said.
Diallo sparked speculation he was set to link up with his Old Trafford team-mates this week after posting a picture of himself on a plane with his bags packed, with some outlets reporting he was jetting out to Rome to finalise his work permit.