Sources tell TMZ, Kim’s currently house shopping in several exclusive gated communities in the L.A. area — including Bel Air … and Mulholland Estates, where both Charlie Sheen and Paris Hilton own houses.

She hasn’t made up her mind yet — but we’re told Kim now refuses to live in any house that doesn’t have round-the-clock gated security.

TMZ broke the story — cops were called to Kim’s home late Saturday night, when a man showed up on her property with a bunch of luggage and rang the doorbell … insisting Kim invited him to stay with her.