Sussex Police said they would like to speak to the two people caught on camera, who made off with the cat on Brunswick Street East on Sunday, December 4 at 11.52pm.
Mr Cheeky’s owner Ollie Wilson, said he discovered the cat was missing the following morning, when he didn’t turn up for his breakfast.
Mr Wilson said: “We have been looking for Mr Cheeky for a week, putting up posters and appealing for help through the Brighton People Facebook page, but only realised he had been snatched when our neighbour was able to check his CCTV footage and found the shocking evidence of Mr Cheeky’s abduction.
“We are devastated by his loss - and want him home by Christmas.”
A Facebook appeal by Mr Wilson’s partner Laura King has had almost 1,000 shares, and the pair hoped Mr Cheeky would be returned by Christmas.
“I would appeal to them to bring Mr Cheeky back,” said Mr Wilson.
He described the two people in the CCTV, and said: “A man - mid-to-late 20s, white, around 5ft 8in tall, of stocky build, with short brown hair, shaved at the sides, wearing a black jacket, light jeans or Chinos and deck shoes - approached Mr Cheeky, bending down to stroke him.
“A woman - around 5ft 6in tall, wearing a long padded black coat with a fur-lined hood, knee-length dark dress and black low-cut ankle boots with light patterned leggings or similar and carrying a supermarket plastic bag - appeared, bent down around four feet from the man and enticed the cat to her.
“The man approached Mr Cheeky from behind and grabbed him with both hands. The man stood up and looked to the left and to the right, up and down Brunswick Street East, to see if they were being observed.
“The woman also stood up, and together they made their escape, walking down Brunswick Street East and turning the corner, to the left, in the direction of Waterloo Street and the seafront.
“Mr Cheeky was wearing a yellow collar and he has a chipped upper right fang.”
Investigating Officer Zoe Ayres said: “Mr Cheeky is micro-chipped and is missed dearly by his owners. We are appealing to anyone who might recognise the man or the woman or have information as to the location of his whereabouts.
“I would also like to appeal to the people in the video as our main priority is to get Mr Cheeky back safe with his owners. He is probably very distressed being away from his normal surroundings and it is obviously very upsetting for his owners.”
Anyone with information is asked to email [email protected] or call 101 quoting reference number 735 of 11/12.