Neither will feature for the Gunners at Goodison Park, as Arsene Wenger's side chase three valuable points against tough opponents.
But both have taken to social media to wish their team-mates all the best.
Walcott says he will be watching the big game, while Podolski says his thoughts are with the Arsenal team, who he has urged to bring the three points home.
I won't be present in person but my thoughts are there with you lads. good luck at the match, go and represent, bring us the 3 points #Poldi— Lukas-Podolski.com (@Podolski10) August 23, 2014
Walcott is yet to return from a long-term knee injury but is far along in the recovery process.
World Cup winner Podolski, however, has been linked with a move away from Arsenal this summer, with Galatasaray initially touted as a destination and then Wolfsburg.
Following the Everton game, Arsenal host Besiktas in the second leg of their Champions League play-off next week. Wenger's side drew the first leg 0-0 and beat Crystal Palace 2-1 in their Premier League opener last weekend.
Next up for the north London side in the league are Leicester City - after their tough test at Goodison, of course.