The plan was crude, and in terms of immediate success, effective. But the "brazen" bloke who snatched a five-carat diamond worth more than A$300,000 from a Sydney jewellery shop maybe didn't quite think the whole plan through.

He's being urged to hand himself in, with police revealing he's been snapped in living colour in CCTV footage - and they've circulated it far and wide.

The man visited the flagship Cerrone Jewellers store at Martin Place on Monday, before returning on Tuesday and asking to see the stone.

It's thought he used Monday's visit to study the stone and have a copy made.

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After asking to see the stone on Tuesday, he then switched the uncut diamond with a replica of lesser value while the employee's back was turned, then left the luxury store.

The cubic zirconia he switched for the real thing is comparatively worthless.

"It's fairly brazen," NSW Police Inspector John Bamford told reporters in Sydney on Friday.

"It's something that we wouldn't normally see."

Releasing the CCTV footage of the accused thief, police described him as being of Asian appearance with a slim build and short black hair.

"The best thing that the man could do would be to hand himself in to Day Street Police Station," Inspector Bamford said.

He wouldn't comment on how the stone was swapped, nor speculate on whether the man may have been a professional or an opportunistic thief.

Shop manager Alison Kotevski told AAP staff were doing everything they could to retrieve the precious stone and catch the criminal.

He told the staff member he wanted to look at large stones and needed to make a purchase before the end of the week," she told The Daily Telegraph.

When staff realised the switch had been made, they contacted police.