Earlier this week the Foxes trio were named on a six-man list for the PFA Players' Player of the Year award alongside Harry Kane, Mesut Ozil and Dimitri Payet, and the same six players are in the frame for the Facebook honour.
Leicester, who are seven points clear at the top of the Premier League with five games remaining, have received 10 nominations across seven categories including Best Premier League Club and Manager of the Year.
Tottenham, their nearest challengers, have nine nominations while Watford's impressive campaign has been recognised with five nominations.
Young Player of the Year will go to Dele Alli, Eric Dier, Ross Barkley, Anthony Martial, Raheem Sterling or Hector Bellerin, while Claudio Ranieri, Mauricio Pochettino, Eddie Howe, Mark Hughes, Quique Sanchez Flores and Slaven Bilic will contest the manager award, with each of their individual teams also up for the club prize.
Voters will also decide on a best XI of the year in a 4-3-3 formation, with the likes of Troy Deeney, Odion Ighalo and Charlie Daniels included alongside the names in the running for the individual awards.
Fans have until Friday 29 April to cast their votes via Facebook, with the winner announced on 9 May at a London ceremony featuring former England manager Glenn Hoddle.
Player of the Year nominees: Riyad Mahrez, Jamie Vardy, Mesut Ozil, Harry Kane, N'Golo Kante, Dimitri Payet.
Young Player of the Year: Dele Alli, Erc Dier, Anthony Martial, Hector Bellerin, Ross Barkley, Raheem Sterling.
Premier League club of the Year: Leicester, Tottenham, West Ham, Bournemouth, Watford, Stoke.
Manager of the Year: Claudio Ranieri, Mauricio Pochettino, Quique Sanchez Flores, Eddie Howe, Slaven Bilic, Mark Hughes.