After a 12-year playing stint at Old Trafford which delivered 464 appearances, five Premier League titles and a Champions League crown - Carrick took up the role on the coaching staff of the Premier League giants.
However, since his retirement from football, the former Red Devils midfielder has been offered a baptism of fire in his new post as Mourinho's assistant.
The current struggles at United have seen plenty of questions raised over the suitability of the Portuguese tactician in his current role.
The likes of Arsene Wenger, Zinedine Zidane and Antonio Conte have been a some of the various names linked with the hot-seat but Carrick insists he is not looking to succeed the three-time Premier League winner.
"I don't want to throw that out there and say I'd want to be United manager," the former England midfielder told the Times.
"It would be amazing to be a manager, but I am not in a position to call that.
"It's not fair or respectful to be going down that route at this stage, it's gold dust having Jose there to draw on what he's doing and learn from him.
"I'm really enjoying it. It's a role that I never thought at this stage of my coaching career that I would get.
"I'm not there as an intern to try and just learn. I'm there to do a job as well and at the same time try to improve myself," Carrick added.
"It's kind of about learning what works for certain lads. Do they need an arm around the shoulder or a bit of a dig in the ribs to liven them up? Those are the skills of coaching and managing.
"I'm not blasé enough to think that I'm going to be a manager. The truth is: I don't know.
"I'm not chasing it. I'm in a fantastic position right now. I'm not looking to get out of that position any time soon because I want to do something else."