England forward Palmer, 22, joined Chelsea from Manchester City on 1 September last year and enjoyed an excellent Premier League season as he contributed to 33 goals, scoring 22 times.
He and Saka, who is also 22 years old, then provided a youthful spark for England during their run to the Euro 2024 final.
Representing Manchester United on the PFA men’s shortlist are Kobbie Mainoo and Alejandro Garnacho, the team’s FA Cup final goalscorers.
Midfielder Mainoo, 19, developed into an important part of Erik ten Hag’s first team and went on to feature in England’s Euros campaign.
Mainoo also scored the second goal against Manchester City as United won the FA Cup final 2-1 at Wembley in May.
Winger Garnacho, who got the first goal in the cup final, was a threat on both flanks for United last season as the 20-year-old Argentine forward scored 10 goals in all competitions.
Michael Olise, who moved from Crystal Palace to Bayern Munich in the summer, is also on the PFA list.
The 22-year-old attacking midfielder scored 10 goals and provided six assists in 19 league appearances during 2023-24 before moving to Germany.
Brighton and Hove Albion’s Joao Pedro completes the nominees.
The Seagulls’ 22-year-old Brazilian forward scored 20 goals in all competitions.