England worldwide Rashford, 22, enjoyed a terrific campaign that also saw him register eight assists in the league.
United's contingent include their lethal front three of Rashford, Martial and Greenwood.
Alexander-Arnold is the only player to be nominated for both awards.
Rashford, 22, scored 17 goals and assisted seven others in 31 league games, while Martial, 24, bagged 17 goals and six assists in 32 appearances.
Klopp will be expected to win the managers' award after guiding Liverpool to their first title in 30 years and finishing with 99 points, 18 ahead of Manchester City in second place. The pair featured heavily in their first ever Premier League seasons.
Manchester City's Kevin De Bruyne was also included after a spectacular season that saw him deliver 20 assists, the highest record in the league, in addition to scoring 13 goals with the Citizens.
Jürgen Klopp has been shortlisted for the Premier League's Manager of the Season award.