While a change of management has done little to improve Tottenham's fortunes, Palace have thrived since replacing Patrick Vieira with Hodgson.
Spurs have seen their Champions League hopes fade with some heavy thrashings in a four-game winless run.
In a blink of an eye Antonio Conte and Cristian Stellini have been sacked in recent months, with Ryan Mason now in interim charge.
The atmosphere around the North London club appears toxic at the minute but Hodgson knows their players can come alive at any moment in time.
“I think the danger for all teams that go to (Tottenham Hotspur Stadium) is that you’re up against a good team with very good players,” he said. “I think Harry Kane is very close to world class, if not in my opinion fully deserving of it.
“There’s a lot of players in their team as well who have got incredible ability. They’re still vying for a Champions League place, we know how difficult a game it will be.
“Crystal Palace when I was at the club didn’t go to Tottenham and win matches, so if we do that it will probably be a first for me I should think.”
Palace have won four out of six games since Hodgson's return to ease their relegation fears and the former England manager wants his charges to keep going.
“I’m hoping more from my point of view to finish the season well,” he said. “I think it’s been a very good six games and 13 points is an excellent reward from six games, but I’d like that to be a good reward now after 10 games and that would be dependent on how much drive and ambition players have.
“I can’t guarantee the players will maintain their desire, but they’ll be given every opportunity
“We need to keep winning and to win you need the lot. You need the desire, the attitude, focus, preparation, quality of attacking play, quality of defending play. You need to be switched on at all times over the course of the game, you need to defend set-plays well, you need to use your own set-plays very well and then you need that little bit of luck.”
