Wearing a polo neck sweater, dark jeans and black Nike sneakers with a designer satchel casually slung over his shoulder, the man made himself comfortable in the luxury store on Tuesday morning and asked to see some of the merchandise.

He allegedly viewed an unset five-carat diamond worth $300,000 before switching it for a similar looking stone of much lesser value.

He then allegedly left the store with the genuine diamond, walking out into busy Martin Place.

Police have released CCTV footage which shows the man outside the store before being let in and taking a seat at the counter.

After he walked out of the store, staff realised the stones had been switched and contacted police.

Cerrone retail manager Alison Kotevski said the calculated nature of the alleged robbery made her feel "sick".

She said the man went into the store on Monday and spent some time looking at the stone before returning the following day.

"We think he studied the diamond and had a copy made before coming back to the store on Tuesday," she said.

Police established a crime scene in the shop, which specialises in high-end designer jewellery, and conducted a forensic examination.

Sydney City Local Area Command officers are investigating the alleged theft and have appealed for public assistance in identifying the man.

The jewellery business has been a target for thieves in recent years with its Leichhardt headquarters, the House of Cerrone, robbed of $3 million worth of jewellery in 2004.

The gun-toting thieves used sledgehammers to smash through security doors and forced seven staff and two customers to lie on the ground while they stole the goods, including earrings once worn by singer Delta Goodrem.

In early 2000, the House of Cerrone was robbed three times in three months, with one haul reaping $2 million in diamond jewellery and designer watches.

Anyone with information about the Martin Place incident can contact Crime Stoppers on 1800 333 000.