McCarthy and Distin on the road to recovery
Roberto Martinez's side are in the middle of a 12-day break, having been knocked out of the FA Cup prior to this weekend's fourth round ties, and have made the most of their time off with a training camp in Qatar.
McCarthy, a starter in just two of Everton's last 10 league games due to a persistent hamstring complaint, has joined in with training sessions in Doha.
And the Republic of Ireland midfielder is now expected to feature against a Palace side boasting four wins in succession under new manager Alan Pardew.
Sylvain Distin is also making good progress in his recovery from a groin problem and could be involved at Selhurst Park.
Martinez told Everton's official website: "Sylvain Distin and James McCarthy are really progressing a lot in this warm weather and that's really positive news.
"They have both joined the group in training and have come through really well.
"I see James as being fully fit now but we will assess everybody before the Crystal Palace game.
"This week has allowed James to build up his fitness levels and I do expect him to be fully fit and ready for Crystal Palace."
Everton lost at home to Palace in September and are level on points with Pardew's side.