Carrick took interim charge of United in January, replacing Ruben Amorim at the helm and has since guided the side up the table and into the top 4.
The former midfielder has led United to six wins, one draw and one defeat after eight games in the hot seat and reports suggest that he will take the job permanently if he keeps his fine form up.
Speaking to talkSPORT BET Casino, Nevin believes the club should hand Carrick the job now as long as he doesn’t slip up.
“Can't see it happening, can't see it happening (Man Utd letting go of Carrick). As we speak just now, it would need to be a complete and utter shock, I mean, they could lose a lot of games if Bruno got injured or that, and they are over-performing.
“I'll tell you exactly what I'd do. I would say to them quietly, 'Look, keep it going till the end of the season. If you don't make a mess of it, the job's yours. So keep it going.'
“So you've got yourself a get-out-of-jail-free card, and you know who's going to be available. There are managers, there are good managers, there are lots of them. But he just seems like a nice fit, doesn't he?”
United are third in the Premier League table, putting them on course to qualify for the Champions League which would never have become possible under Amorim.
Carrick is the favourite to become the next permanent manager as he prepares to take on Aston Villa this weekend where a win would cement his side’s spot in the top 4 even further.