According to talkSPORT, the interim manager has turned down the chance to become a part of Carrick’s team once he take the reigns to The Red Devils.
However, Fletcher will reportedly remain at the club in his previous role as the U-18s head coach after his stint as manager is over.
The supposed decision comes after discussions on Monday (01.12.26), during which Fletcher was reportedly offered a position on the new backroom team but chose not to continue with the first-team setup.
It follows his two-match spell in temporary charge after Ruben Amorim was sacked earlier this month.
Fletcher oversaw a 2-2 Premier League draw away at Burnley before Sunday’s (01.11.26) 2-1 FA Cup defeat to Brighton at Old Trafford ended United’s involvement in the competition.
With earlier exits from the Carabao Cup and Europe, the club now has only Premier League fixtures remaining this season.
Fletcher will now return to his academy role ahead of United’s FA Youth Cup tie against Derby County next week.
Fletcher had been the Under-18s manager since July, having previously worked as a first-team coach under both Amorim and Erik ten Hag.
United’s Under-18s currently sit second in the U18 Premier League North, four points behind leaders Manchester City.
The squad includes Kai Rooney, son of club legend Wayne Rooney, as well as Bendito Mantato, who made his Premier League debut in December.
After the Brighton defeat, Fletcher urged United’s senior players to “dig deep” and rebuild their confidence following another disappointing result.
Speaking after the game, he said: “It was mixed really. I thought we started okay, then the goal knocked the stuffing out of us and we didn’t really create a tempo.
“We didn’t play enough balls in behind and test them. I think our passing was quite slow.”
Brighton took the lead through 21-year-old winger Brajan Gruda before former United striker Danny Welbeck doubled the advantage, increasing the sense of frustration inside Old Trafford.
United responded late on through striker Benjamin Šeško, but were unable to find an equalizer.
Fletcher added: “I thought we created enough chances, but to go 2-0 down was disappointing.
“When we got back to 2-1, I thought, ‘Here we go.’ The crowd was up, the energy was up, but ultimately we couldn’t get over the line.
“I think you can see that the players are fragile and they need to build themselves up. Because it’s up to them now, they’ve got to respond.”