Despite having struggled this season, Puel believes that West Ham will be eager to produce a response at the London Stadium.
"Their fans want a reaction so we have to be careful," the Frenchman told Sky Sports News. "We know this team and they will want to show their qualities at home.
"When a new manager arrives, there is always a possibility for different players to show their qualities and try and win their place.
"It will be a strong game against them and we have to keep our focus because it will be a crucial game for us.
"I know [Moyes] from last season with Sunderland. After our game, I wish success for him and for his team. Just not on Friday!"
Leicester currently sit 12th in the Premier League table, while West Ham are in 18th place.