United are seeking to sell one of their centre-forwards as they seek to bring in two more attacking targets after the arrival of Matheus Cunha from Wolves.
Il Corriere dello Sport says United are now actively seeking a buyer for Hojlund, while deciding to keep hold of Zirkzee.
Inter Milan are already in contact with United for Denmark international Hojlund.
The Nerazzurri want to set up a loan-to-buy arrangement, while United would prefer a straight sale for £35-40m.
For his part, Hojlund would be happy to stay at Old Trafford.