The Ivorian forward has been the star man for the 'Eagles' so far this season, but missed out on the game against Southampton due to a groin issue.
Crystal Palace lost that game and his absence was noticeable, but his manager Roy Hodgson hopes that he will be able to play in the game against Huddersfield this season, which will be a vital fixture.
"It was debatable whether he should train or not, but he was anxious to try, and the same applied to James Tomkins, so it was really good to see them back out with us again.
"But we will have to wait until tomorrow to see how they react to tomorrow's training session and see if they are going to be available, because both [players], if we listen to our medical department, are coming back early, if not as early as should have been expected."
With the fitness of Zaha unknown, Hodgson will look of the rest of the squad to step up in his potential absence.