The remaining nominees are Keith Andrews (Brentford), Andoni Iraola (Bournemouth) and Regis Le Bris (Sunderland).
Fans will be able to vote for Carrick, with their selections combined with a panel of experts to decide the final outcome.
He is also the only shortlisted candidate who has not been in charge for the full season, underlining the speed of his impact. Carrick previously won the Premier League Manager of the Month award for January.
Since being appointed head coach of Manchester United in January, he has overseen a rapid climb from sixth to third in the Premier League table.
His record stands at 10 wins from 15 matches, with only two defeats, and United have collected more points than any other side in the division over that period.
Key victories have included wins over Arsenal and Manchester City early in his tenure, as well as later triumphs against Liverpool and Aston Villa.
An away win at Chelsea carried extra significance, given United had only beaten them once in the league since the 2012/13 season.
A dramatic 3-2 victory over Liverpool secured UEFA Champions League qualification for UEFA Champions League with three matches remaining. United can now secure a top-three finish with at least a point against Nottingham Forest on Sunday.
