The producers of The Ultimate Joker website have argued that Ledger's BAFTA-winning portrayal of the supervillain was so perfect that no attempt should be made to replace him.
They said: "It's impossible to imagine, impossible to draw or dub much less repeat the performance.
"That's why efforts to find one should simply cease. The Joker must die now and forever.
"Now is the time for him to rest in peace as Ledger has ennobled the honourable villain."
They added that the "ultimate Joker" deserves the homage of having the character retired from future films.
Director Terry Gilliam recently described Ledger as a "genius" and the best actor of his generation.