The 35-year-old has only featured six times this season, with Mourinho insisting the Englishman can only be used sporadically.
It was reported that Carrick, following an excellent performance against Swansea City (his first Premier League start of the season), would be offered another extension as part of an option on his existing contract.
Neville, speaking on Sky Sports ahead of Man United’s clash with Arsenal on Saturday, insisted the 53-year-old needs to deploy Carrick on a more regular basis.
“Carrick is almost never going to be star of the show, but I always get the feeling that when Michael is in the team, the team play better,” he said.
“That was the feeling when I was there, and since I’ve left.
“He has the habit of bringing the best out of other players. That’s through the control he brings, the composure, the experience, the defensive and positional play that some people don’t always spot because it’s not a sliding tackle or aggressive header.
“You won’t find many people that have a bad word to say about him, he’s a fantastic player, and the big thing is he makes the team tick a lot better.
“I’d be surprised if we didn’t see him play on Saturday. We’ve had an international break where he isn’t involved, he’s had the time for preparation, and could be important for United on Saturday.”
With Carrick in the side, United suddenly morph in to a completely different outfit. Performances under Mourinho this season have been characterised by a sense of uncertainty – a lack of direction, almost. The pieces are all there, but how do you put them all together.
Needless to say, the Englishman’s presence serves as an emphatic response to this query. He is – and always has been – the omnipresent reference point at the base of midfield, calmly and efficiently dictating proceedings, and in turn giving players the freedom to express themselves and fully implement Mourinho’s vision.