Carrick, 45, will take charge of Manchester United’s Premier League clash with Chelsea on Saturday (October 31), despite their shocking start to the season.
Regardless, Carrick is still under immense pressure at the club and rumours continue to circulate about who could take over should United pull the trigger.
The likes of Eddie Howe, Antonio Conte, and Nagelsmann have all been linked with the job.
TalkSPORT understands that Howe is currently the frontrunner to replace Carrick in the Old Trafford dugout, but nothing is concrete yet.
German football journalist Constantin Eckner believes Nagelsmann can’t be ruled out.
Eckner told talkSPORT on Tuesday: "Nagelsmann was already interested in the Manchester United job in the past, but the timing was never really there to join Manchester United, despite them hiring a new manager every 12 months or so.
“The (Christopher) Vivell connection is there, these two know each other and Vivell might be pushing for Nagelsmann.
"As far as I understand it, Nagelsmann would be interested, but he's not the frontrunner. Eddie Howe is the frontrunner, but Nagelsmann is ready.
“The DFB, the German Football Association, bought him out of his contract. So there is no hurdle to take.
“He can join whoever he wants, whilst Manchester United have to pay Newcastle United to get Eddie Howe as their manager right now."