Il Corriere dello Sport says Inter are keen to set up a loan deal with United for the Holland international.
Inter chief Piero Ausilio plans to approach United about a loan-to-buy arrangement for next season.
The idea is to give Zirkzee a full season to prove himself and shake off this term's issues at Old Trafford.
Zirkzee's wages of around €3.5m-a-season plus bonuses, would also fall within the economic parameters of Inter, in line with the new "vision" of owners, Oaktree.