This comes despite the fact he trained alone in Israel ahead of their opening European Championship group game against Italy on Wednesday.
Manchester United winger Zaha arrived later than the rest of the group, but the Football Association have said this was always the plan.
"He shouldn't be a doubt," Pearce told Sky Sports News.
"Obviously he has played a real full season with the play-off final last Monday and the plan was to put him in, do the warm up and then work with the physios.
"Then we will have a look at him and see where he is regards of fitness but we should not have a problem with him.
"He is in top form, his contribution all season for Palace, getting his move to Manchester United and then helping them win the play-offs.
"He has been outstanding, he has left a club back in the Premier League and is now with Manchester United but he will be a cult hero back at Palace."