The 23-year-old scored on his debut for the Red Devils against Fulham, coming up with a late winner against Marco Silva's side, with Man United making the perfect start to their new Premier League season.
However, the striker has not scored in his last 11 appearances for Erik ten Hag's team, drawing another blank in Thursday's 1-1 draw with Fenerbahce.
Zirkzee did come up with the assist for Christian Eriksen to score against the Turkish giants, but his overall performance level has been criticised, and there has been speculation surrounding his future.
Juventus have been linked with the Dutchman, and it has been suggested that Zirkzee would be open to returning to Serie A in January, having impressed for Bologna ahead of his switch to Old Trafford.
Zirkzee 'not interested in Man United exit'
However, according to German journalist Florian Plettenberg, the forward has 'no intention' of departing in the winter window, with the Dutchman confident that he can establish himself at Old Trafford.
Plettenberg has called the speculation surrounding his future 'fake news', while it is believed that Man United head coach Ten Hag remains confident that Zirkzee can be an important player for the club.
Zirkzee scored 14 times and registered nine assists in 58 appearances for Bologna, while he also managed four goals and one assist in 17 outings for Bayern Munich in the early stages of his career.
The Dutchman was Man United's number one striker in the early stages of the campaign, but he is now behind Rasmus Hojlund in the pecking order following the number nine's return to fitness.
Should Man United persevere with Zirkzee?
It is still extremely early, and there have been positive signs during stages of his time at Man United, but it does appear that Zirkzee is more suited to a number 10 position rather than a centre-forward role.
Zirkzee's lack of pace is a problem when it comes to his spot as a striker, while he has also missed a number of chances this season, so there have been questions over his ability to finish.
The Dutchman is a technically gifted player, though, and he has proven in certain matches that he can bring other teammates into play, with the best example of that potentially coming against Crystal Palace last month.
Zirkzee must be given at least the season to prove himself, but it would not be a surprise if his future was revisited next summer, with a return to Italy certainly possible if he continues to find it difficult in English football.