Chelsea's Eden Hazard, Manchester City midfielder Yaya Toure and Adam Lallana of Southampton complete the six-strong list for the award which will be presented in London on April 27.
Sturridge and Hazard are also up for the Young Player award along with Arsenal's Aaron Ramsey, Raheem Sterling of Liverpool, Southampton full-back Luke Shaw and Everton's Ross Barkley.
Liverpool captain Gerrard is bidding to win the award for the second time in his 15-year professional career after scooping the accolade in 2006. He is also a former winner of the Young Player award back in 2001.
His team-mate Suarez is an early favourite for the award in a season where the Uruguayan has scored 29 league goals. Suarez's strike partner Sturridge has also been in prolific form for the club this term, scoring 23 goals in 30 matches in all competitions.
Hazard has reached double figures in both goals and assists for Chelsea this season, scoring 17 goals and contributing 10 assists to Jose Mourinho's side in all competitions.
Toure has enjoyed his most productive season in his four-year Manchester City career to date, scoring 22 goals and directly assisting a further eight for the club in all competitions.
Lallana has impressed at Southampton this year and his club performances have seen him earn international recognition this season with Roy Hodgson handing the 25-year-old midfielder his England debut against Chile in November.
Liverpool also dominated the shortlists for the women's awards. Liverpool Ladies trio Natasha Dowie, Lucy Bronze and Nicole Rolser are all up for the Women's Players' Player of the Year award.
Arsenal Ladies duo Siobhan Chamberlain and Jordan Nobbs are also in the running along with another former Arsenal player Kim Little, who is now at Seattle Reign.
Bronze and Nobbs are also shortlisted for the Young Player award alongside Manchester City's Izzy Christiansen, Everton's Alex Greenwood, Liverpool's Martha Harris and Danielle Carter of Arsenal.