The rest of the Carabao Cup quarter-finals are taking place on December 16 and 17, when they were originally scheduled to be played.
The original date of December 16 would have forced Palace to have played three games in the space of five days.
The Eagles are hosting Manchester City in the Premier League on December 11 and Finnish side KuPS in their final Conference League league phase tie on December 18.
Arsenal had argued that December 16 was a better date for the tie with Palace, because playing on December 23 means both sets of players will have just one day’s rest.
Arteta has now revealed how he hopes that the game with Everton on December 21 is moved to give Arsenal more time to prepare.
“Well, hopefully, in the end they will move our Premier League match, because to play two days later doesn’t make any sense, obviously,” said Arteta.
“We will now decide the date. I am sure they will change the Premier League date, as well.
“I think we were very clear what was the best thing, the more logical date to play.
“They bring a different date, so I am sure we will have to adapt to that. I think, as I said the other day, I am sure we apply the principles of first all equality and the same chances for every club. So, hopefully, it will be fair.”