A man has allegedly stolen a five-carat diamond worth around $300,000 from a Sydney jewellery store by replacing it with a fake he hid in his pocket.

Staff at Cerrone Jewellers said the man asked to see the diamond when he was at their Martin Place store on Monday morning.

He went back the next day and swapped the real diamond for a cubic zirconia, otherwise known as a costume diamond, worth virtually "nothing".

After swapping the stones, the man calmly left the store with the five-carat diamond hidden in his pocket, Cerrone Jewellers retail manager Alison Kotevski said.

Police allege a man viewed an unset five-carat diamond, a similar size to this one. ( Instagram: clemenceellery )

"He got the opportunity unfortunately and he swapped the stones and he was quite cool, calm and collected and then left the store telling the staff he would return with a friend to purchase the stone," Ms Kotevski said.

The man is described as being of Asian appearance with a slim build and short black hair.

In CCTV footage released by NSW Police on Friday, the man is shown wearing a grey jumper, dark-coloured pants, black Nike sneakers and carrying a shoulder bag.

Ms Kotevski said the theft had been devastating for the store.

The Cerrone Jewellers store in Sydney's Martin Place. ( Instagram: Cerronejewellers )

"Obviously we've got all the security in place to stop and prevent these things happening and we've got wonderful CCTV footage and everything like that," she said.

"We do everything we can to prevent these things but every now and then obviously something does happen."

The stone is Gemological Institute Of America (GIA) certified and carries an inscription on the side of the stone with the GIA logo and the number.

Cerrone Jewellers said the stone was traceable.

"We are just hoping that if he does try to sell it that someone honest finds it," Ms Kotevski said.