Both Britain's Sun and Daily Mail newspapers reported that an anonymous seller had been in contact offering the images for sale.
The Sun said the cyber thief -- who got in touch via an encrypted messaging service and used the pseudonym "Crafty Cockney" -- claimed to have images that also included Middleton at a wedding dress fitting and nude photos of her fiance, financier James Matthews.
The seller demanded "a minimum of £50,000" (around $65,000) within 48 hours, as of Friday afternoon UK time, both newspapers said.