He has been linked with an exit for much of the past year and remains a potential departure when the transfer window reopens. Fiorentina and Everton both made attempts to sign him on deadline day, but United ultimately saw little advantage in letting him leave.
Zirkzee has not started a Premier League game yet, but he has featured in the past three matches and sources suggest Carrick retains faith in him.
He does not intend to lose the Dutchman midway through the season - particularly with United facing fresh uncertainty over their attacking options.
Benjamin Sesko has suffered another injury setback after showing encouraging signs of form before the international break. The Slovenia international withdrew from duty, and there is still no clear picture of the severity of the problem, with suggestions that it could be connected to an earlier issue that previously kept him out.
United are taking a cautious approach to his recovery, leaving Carrick with fewer established options through the middle. Bryan Mbeumo took the lead role this weekend, but Zirkzee was introduced from the bench for 31 minutes against Tottenham and was among United's better performers on the day.
His contribution offers a reminder of what he could bring if given a more consistent opportunity, particularly at a time when United are still assessing whether their current attacking options are sufficient.
Zirkzee is understood to remain committed to turning his situation around at Old Trafford and continues to work hard to convince the coaching staff that he can play a bigger role.
Napoli and AC Milan have been linked with the forward, however, and interest from Italy could return if United decide he is surplus to requirements.
There are still significant considerations for United, who have been putting thought into whether to recruit another forward in January.
That decision could either push Zirkzee further down the pecking order or prompt the club to reconsider which players they can afford to lose.
Additionally, we reported on Friday how Carrick's own position remains uncertain.
United have taken just six points from their opening six games under him, and the performance against Tottenham did little to ease scrutiny of the team's progress. Whether he remains in charge by January could influence the club's transfer strategy and the opportunities available to Zirkzee.
For now, though, the forward's departure is far from inevitable.
United were unwilling to sanction an exit on deadline day, and with Sesko's fitness unresolved and Carrick still backing him, Zirkzee could yet be given another chance to revive his Old Trafford career.