The six-man shortlist, which also includes former Crystal Palace winger Michael Olise and Brighton's Joao Pedro, was announced on Monday following a vote by the members of Professional Footballers' Association.
The 2024 prize is particularly competitive, given the output of the nominees last season, though Palmer will be considered the favourite after his stunning debut campaign at Stamford Bridge.
The 22-year-old scored 22 goals and recorded 11 assists in only 34 Premier League games for the Blues, who toiled for much of the campaign.
Elsewhere, Garnacho and Mainoo both enjoyed stellar seasons at Old Trafford, with the latter coming out of nowhere to establish himself as a key player for both club and country.
Mainoo made 24 league appearances for the Red Devils after recovering from an ankle injury in preseason, while Garnacho chipped in with seven goals and four assist from his 36 top-flight outings.
The duo were fittingly on the scoresheet as United earned a shock 2-1 victory over bitter rivals Manchester City in the FA Cup final last term.
In any ordinary season, 2023 winner Saka would be a shoo-in to claim the prize, having scored 16 goals and provided nine assists for the Gunners as they mounted a serious challenge for the Premier League title.
The 22-year-old also scored four times in the Champions League for Mikel Arteta's side. Saka is now only three strikes away from a half century of goals in the Premier League.
Rounding out the nominees are Bayern Munich winger Olise and the Seagulls star Pedro. Olise completed a £52million move to the German giants before he joined up with the French Olympic football team for the tournament in Paris.
The event ended in heartbreak for the hosts, who were beaten by Spain in the gold medal match. Still, it completed an impressive season for the 22-year-old, who hit double figures in the Premier League for the very first time.
Michael Olise (left) and Joao Pedro (right) are surprise finalists for the award, though they both excelled for their respective sides last term
Pedro was only one goal shy of that mark in his maiden season at the Amex following a big-money move from Watford. The striker might have eclipsed that tally if not a hamstring injury which sidelined him for six matches.
The winner of the PFA Young Player of the Year award will be announced on August 20.