Palmer, 65, was found dead three years ago in the garden of his remote woodland home in South Weald, Essex.
His partner has said she feels haunted every day that he was stalked like an animal by his killer.
Police believe it was a professional contract killing which happened in the only part of the garden not covered by CCTV.
Detectives think the gunman watched Palmer until he went to make a bonfire to burn some old documents and then jumped over the fence.
Palmer gained his Goldfinger nickname after being acquitted of handling gold bullion in the £26m Brink’s-Mat raid in 1983.
He was once described as Britain’s richest criminal and was thought to have been worth £300m.
On 24 June 2015, he was shot six times at close range – in the right elbow, right breast, right upper abdomen, top of the back, left renal area and left bicep.
Experts believe it is possible that three of the bullets were fired into Palmer while he was standing and three while he was lying on the ground, with the gunman walking around him and firing.
Essex Police have released photos of the hole in the 5ft (1.5m) high fence panel, believed to have been scratched with a nail or another sharp object. They also released an image of one of the bullets.
Christina Ketley, Mr Palmer’s partner, said It haunts us every day to think that whoever was responsible was clearly watching John, stalking him like an animal before so brutally and callously ending his life.
Losing a loved one is hard enough but in this case we have the added stress of not only not knowing who did it but why.
Detective Chief Inspector Stephen Jennings said Palmer had links to some of the people convicted over the £14m Hatton Garden raid in 2015 and had been due to stand trial in Spain over alleged real estate fraud.
My belief is the person responsible in arranging this is someone very high up in the criminal underworld and we would expect, if finances were used to purchase this killing, you’re talking about a large sum of money, he said.
A £100,000 reward has been offered by his family, with the support of Crimestoppers, for information leading to the arrest and conviction of his killer or killers.
DCI Jennings said there was no reason for us to believe that the money put up by members of John’s family is the proceeds of criminality.
Palmer’s body was discovered in the garden by his son’s then girlfriend.
Officers originally thought he had died of natural causes because of recent keyhole surgery to his chest, but it later emerged he had been shot.
Detectives are continuing to appeal for information about a man and woman seen near Palmer’s home the day before the murder.
News Source SkyNews