Vivell has an important role in United's recruitment structure and is understood to be among the figures who could influence the club's choice of head coach should the hierarchy decide to part company with Carrick.
The current manager has come under increasing pressure following a poor run of results, although Tuesday's dramatic 3-2 Champions League comeback victory over Roma offered some relief.
United had previously endured a nine-game sequence without a win, with heavy defeats against Como and Bournemouth adding to the scrutiny. Their subsequent 2-0 loss to Chelsea did little to settle the situation, leaving the forthcoming fixture against Aston Villa an important test before the November international break.
Julian Nagelsmann, Eddie Howe and Brighton manager Fabian Hurzeler have been mentioned as possible alternatives should United make a change. Nagelsmann has a connection with Vivell from their time together at RB Leipzig, where the pair worked in the German club's football structure.
That relationship could give the former Bayern Munich and Germany coach an influential supporter inside Old Trafford. However, reports of interest from Bayern in Vivell have introduced uncertainty over his own future.
Bayern are searching for a replacement for head of scouting Nils Schmadtke, whose departure from the club has been agreed for January 2027. Vivell has emerged as a possible candidate, having previously worked in Germany and built a strong reputation through his recruitment work at Red Bull Salzburg and Leipzig.
He also has an established relationship with Bayern sporting director Christoph Freund, dating back to their time together at Salzburg.
The situation is not straightforward, however. Recent reporting in Germany suggests Vivell is one of the names under consideration rather than an appointment already agreed, with differences within Bayern's leadership over the direction of the search.
For United, the possibility of losing Vivell would be significant at a time when the club are facing uncertainty over both their head coach and the wider football operation.
His departure could also remove a key advocate for Nagelsmann, potentially changing the balance of influence in the managerial discussions. The German's connection with Vivell is not the only factor in any appointment, but losing that internal relationship would be an unwelcome complication.
Carrick's immediate future remains dependent on results, with the Aston Villa fixture looming before the hierarchy reassesses the position during the international break. United must therefore consider not only whether a change is required in the dugout, but also whether the people responsible for shaping that decision will remain in place.
A move for Vivell would give Bayern an experienced recruitment figure, while leaving United with another important position to address during an already unsettled period.