The Dutch forward has started three straight Premier League games, finding the back of the net in last weekend's 2-1 victory over Crystal Palace.
The 24-year-old scored on his United debut but has endured a dismal run since then, netting just three more league goals in 38 appearances as fans grew impatient with the young striker who is set to leave the side.
Now, as reported by Manchester Evening news and Corriere dello Sport, the Red Devils have reported rejected an approach from Italian giants Roma as they try to work out a deal that works for both parties.
The report states that United have rejected an initial offer of a loan with an option to buy, depending on Champions League qualification for the Serie A side who would need to put together the funds to take on the striker.
Zirkzee started against West Ham on Thursday night before being subbed off in the second-half of the 1-1 draw. With the Africa Cup of Nations starting this week he may prove to be even more useful for Amorim who continues to experiment with him in the side.
He is expected to keep his place up front for Monday's visit of Wolverhampton Wanderers, as Benjamin Sesko remains sidelined. The former Bayern Munich protégé has scored just eight goals and set up three more in 57 games for the side and despite him now being essential for Amorim, a January move looks very likely.