A source said: "The Clinton diary hack came at a time when Williams' work with America was of the most sensitive nature.
"It was a diplomatic nightmare for Sir John Sawers, the new director of MI6 at the time."
The paper has also reported that voicemail messages Mr Williams, a maths genius and expert cryptographer, left for family and friends were deleted shortly after his death.
Earlier this month, it was revealed that detectives who investigated the mysterious death believe he was murdered and that his killers then broke back in through a skylight to cover their tracks.
The claim centres on the revelation that part of the forensic equipment placed in the flat after the body was found was moved - despite the fact the building was under armed police guard.
The theory supports his family's suspicions he was murdered by "agents specialising in the dark arts of the secret services".
Mr Williams had been working with the American National Security Agency in Washington before returning to London, where he underwent training and was sent on active operations.
The exact nature of his work remains a closely guarded secret, but sources claim he dealt with equipment that tracked the flow of cash from Russia to Europe.
The technology enabled MI6 to follow money trails from bank accounts in Russia to criminal European gangs. One theory is that Mr Williams had disrupted a mafia ring closely linked to the Russian state.
Cars registered to the Russian Embassy were spotted near his Pimlico flat just days before his body was discovered on August 23, 2010.
Mr Williams was last seen alive on August 15 - a Kremlin car was seen near his property that day.
Other lines of inquiry, also dismissed by the Metropolitan Police at the time, were that he was killed by MI6 or American agents after stumbling on sensitive data, or because he threatened to make secret intelligence public.
There were also claims Mr Williams may have been killed by a lover during a bizarre sex game.
Coroner Dr Fiona Wilcox, who heard the 2012 inquest into his death, criticised MI6 for failing to report that the spy had been missing for a week, saying this caused extra suffering for his family and led to the loss of forensic evidence.
The delay, for which MI6 apologised, also meant a Home Office pathologist was unable to find a cause of death.
Dr Wilcox concluded that Mr Williams's death was "unnatural and likely to have been criminally mediated".
She said she was satisfied "on the balance of probabilities that Gareth was killed unlawfully", as it was likely someone else had put his body in the bag and locked it.
But a year later, Scotland Yard ended a review of the investigation, saying it was more likely Williams had locked himself in the bag and that no one else was involved.
This is despite there being no traces of Mr Williams' own DNA on the padlock of the bag he was found in. His palm prints were not found on the bathtub which held the bag.
Another theory was that Mr William's was poisoned. Former Detective Chief Inspector Colin Sutton was the most senior officer on the scene when he arrived at Mr Williams' flat in Pimlico on August 23, 2010.
He thought the flat was unusually warm when he arrived, claiming the heating was turned up to its maximum setting, possibly to assist with decomposition.
He said: "If he had been poisoned, then the chemical compounds might have vanished by the time toxicology results were conducted."
- Daily Mail
