The injury-plagued Ghanaian has not featured since picking up a thigh problem in the 3-0 defeat to Crystal Palace on April 4 - missing Arsenal's last eight Premier League matches.
The 28-year-old's injury was expected to rule him out for the rest of the season, with Mikel Arteta pessimistic about his chances of featuring before the campaign is over.
A recent report claimed that Partey would remain sidelined for the final-day encounter with the Toffees, but he has since been pictured with the ball at his feet in training.
A short clip released on Arsenal's social media channels shows Partey participating in rondos with the rest of the group, while he also undertook other possession-based exercises at London Colney.
The former Atletico Madrid man seemingly came out of the session unscathed, but it remains to be seen if Arteta is willing to risk him for the visit of Frank Lampard's side.
Partey has consistently struggled with injuries since arriving in the English capital - missing a total of 17 games last season due to hamstring, muscular and hip problems.
The Ghana international then picked up an ankle injury in a pre-season friendly with Chelsea back in August and missed Arsenal's first three defeats of the Premier League season to Brentford, Chelsea and Manchester City.
When fit, Partey has established himself as a key player for Arsenal in the middle of the park, registering two goals and one assist in 24 Premier League matches throughout the season.
However, Takehiro Tomiyasu was nowhere to be seen with the group and is expected to miss out with the muscular issue that he sustained in the 2-0 loss to Newcastle United on Monday.
Arsenal will start the day two points behind Tottenham in fifth place and will qualify for the Champions League if they overcome Everton and if 20th-placed Norwich City can shock Antonio Conte's side.
Should Tottenham and Norwich play out a draw, Arsenal would need to beat Everton by a 16-goal margin in order to pip their North London rivals to fourth place.