Carrick has not only steadied the ship at United since taking over from Ruben Amorim earlier this year, he has transformed the side into a team who are close to securing Champions League football.
The former midfielder won his first four games in charge of the Red Devils and is the leading candidate to take the job permanently when the season concludes.
Speaking to Stake, Evra believes that Carrick should be given a chance despite Paris Saint-Germain's Luis Enrique also being an enticing prospect.
“I'm not talking to the United board or Sir Jim Ratcliffe, but in my honest opinion, with no disrespect to PSG or Nasser Al-Khelaifi, but Enrique would be a dream coach for United. I love the man, I love his philosophy, what he went through in his personal life and overcame it shows his personality. The job he's done at PSG by bringing them a Champions League without Lionel Messi, Kylian Mbappe or Neymar, it's a fantastic job.
“Players would have to work really hard to play for Man United, they'll have to run a lot and I think Enrique would bring that. But, I don't think we should write off Carrick, he's done a great job and we need to give him an opportunity.
“People want an amazing manager for United, but right now, we need someone who understands the club and the players. Enrique is a genius tactician and great with players, but I think Carrick deserves a chance.”
Reports state that United have decided that they want to appoint their next permanent manager before the start of this summer's World Cup and Carrick will be hoping he gets a call to step up and lead the side next season.