Chelsea and Tottenham Hotspurs have two players each on the list.
Kai Havertz, Trevor Chalobah, Dejan Kulusevski, Andy Robertson, Ivan Toney, Harry Kane, Bukayo Saka and Matty Cash are among the players shortlisted.
Havertz enjoyed arguably his best month in the Premier League, registering four goals and one assist to help Chelsea go unbeaten.
Kane also found the back of the net four times for Tottenham Hotspurs and added two assists to his season tally.
Brentford'sToney scored his first top flight hattrick against Norwich City in March before adding two more goals to close out the month.
Saka continued his brilliant form this season for Arsenal, netting a vital winner at Aston Villa. He finished the month with two goals and an assist.
Robertson helped Liverpool keep three clean sheets and also laid on one assist as the Reds kept up the pressure on leaders Manchester City.
Winter signing Kulusevski continues to impress on the right side of Tottenham's attack, laying on three assists in four games for Antonio Conte's side.
Cash scored once for Aston Villa and assisted twice while helping to keep two clean sheets from four matches.
Chalobah played all three Chelsea games in March, scoring once, assisting another and keeping two clean sheets.
Liverpool's Joel Matip won player of the month in February.
Elsewhere, Thomas Tuchel, Jurgen Klopp, Antonio Conte, Brendan Rodgers and Mikel Arteta will contest for manager of the month.
