Rodgers guided Liverpool to five successive victories last month as they collected maximum points, which also included an impressive 3-0 win over Manchester United at Old Trafford.
Martinez looks to be Rodgers' main rival for the gong, with his Everton side having also won all five of their league games in March to keep the Goodison Park club in the hunt for a top-four finish.
Pellegrini's Manchester City team won three and drew the other of their four top-flight games. Like Liverpool, City also recorded a comfortable 3-0 victory away to United.
Stoke boss Hughes had a good March as well, with his Potters side winning four and drawing the other of their games as they continued to close in on their highest Premier League points tally.
The Player of the Month award is dominated by strikers with Luis Suarez, Jay Rodriguez and Romelu Lukaku all in the running, alongside midfielder Steven Gerrard.
Liverpool skipper Gerrard scored four goals in March, including two penalties in the Reds' win at Old Trafford.
His team-mate Suarez hit six goals for the Reds, including a hat-trick in the 5-3 victory away to Cardiff.
Rodriguez hit five goals in five games for Southampton, while Lukaku was on target three times for Everton.
The winner of the awards will be announced on Sky Sports News from 10am on Friday morning.