The military says protesters were the main priority
The Foreign Minister, Renato Ruggiero, said that Italian air space had been closed in response to the threat.
Egyptian President Hosni Mubarak also said there were reports of a planned attack on Mr Bush and other world leaders who attended the summit in July.
Airspace closed
Reports prior to the summit said that the German secret service had passed on information to the Italian authorities about a bomb attack planned by Osama Bin Laden.
There were also reports that Bin Laden's supporters might launch an air attack.
The White House was aware of the threat, said spokesman Ari Fleischer, but he would not comment further.
Italy closed airspace over Genoa during the summit and also over Naples for the preparatory summit which took place there.
"What I know is that intelligence (services) in Italy knew that an air attack was considered to be possible and that was the reason why we closed the airspace in Genoa during the G8 summit," Mr Ruggiero said. Air defences were also established.
But military sources said concerns focused on keeping the thousands of anti-globalisation protesters - some of them violent - who besieged the conference out of the high security "red zone" in Genoa.
The main priority in closing air space, the sources said, would have been to eliminate the potential for anti-globalisation protesters to hang glide - or even parachute - into the sealed off zones where the summits took place.
'Bin Laden connection'
However in the wake of the attacks on the United States, which the authorities there have blamed on Bin Laden's network, others have come forward to say his group planned an attack at Genoa.
Mr Mubarak was quoted as saying that Bin Laden had announced in a communiqué that he planned to assassinate Mr Bush.
And the head of Russian President Vladimir Putin's bodyguard service was quoted as saying that Mr Bush was under threat from the Saudi born dissident.