Luis Enrique would be Owen Hargreaves first choice to replace the sacked Ole Gunnar Solskjaer
Bizarrely, Carrick is effectively the caretaker boss until an interim manager is found to steer the ship for the rest of the season, at which time another, permanent appointment will be made.
Current Paris Saint-Germain manager Mauricio Pochettino and Leicester City boss Brendan Rodgers are seemingly the preferred candidates to take charge of the club long-term, Ajax's Erik Ten-Hag an outside name.
However, all three are currently in jobs and therefore would be harder to entice to Old Trafford before the season's end.
Hargreaves has explained how though he concedes the huge talent of the aforementioned trio, he thinks former Barcelona boss and current La Roja manager Luis Enrique should be the number one choice in the eyes of the United hierarchy.
Pressed on the main contenders to take over at United, Hargreaves said BT Sport: "I think [Pochettino] commands respect, I think he demands work from the players. But all these names are great names.
"Brendan has great experience in the league. Zidane, surely the language barrier has got to be a thing.
"Ten Hag has done unbelievable with Ajax, but they’re the best team in Holland – is he going to be able to dominate the ball over here in the Premier League like he does in Holland?
Owen Hargreaves has had his say on who Man Utd should appoint as their new manager
(Image: BT Sport)
"I think one name that’s not on there, which I’d like to see, is Luis Enrique."
Hargreaves went on to give his reasons behind the claim, citing the Spaniard's feats while in the Camp Nou hot-seat a good a reason as any for United to secure his services.
"If you manage a big football club like Barcelona, and you won the treble there, and then you can go and take a pretty average team to a semi-final [of Euro 2020] in Spain, I think that’s the type of guy [United need]," he explained.
"And he’s only managing the national team, so I think he could come in and do the job now.
"I think he would transform United from a good team into a great team."