In a private briefing to BBC London, the security official said the Olympic Stadium would be the “most sensitive terrorist target in the world”.
Officials are also concerned the Games are being held during the Islamic month of Ramadan for the first time in more than 30 years.
The un-named official added “community-led intelligence” would be key.
Explaining why the Games could be a target, Noman Benotman, a former extremist who knew Osama Bin Laden, said terrorists think it is taking place during a “sacred time”.
“Maybe it’s an opportunity for them to end up in heaven,” he said.
He added: “[An attack] is not acceptable at any time”.
“Terrorism has absolutely no place in the Muslim community and if somebody is going to be going about this sort of activity, of course that is going to be reported to the police.
“Muslims love London just like everybody else,” he added.
BBC correspondent Asad Ahmed said there have been more terror suspects arrested in east London than in any other similar sized area in Europe.
Roy Ramm, a former Met Police commander who specialises in terrorism, said security forces had to be sensitive and effective.
“This has got to be an intelligence-led operation,” he said.
“They’ve got to identify cells which will be plotting to do something.
“If they move too quickly, they can be accused of being oppressive and disruptive, particularly in the month of Ramadan. If they move too slowly, then the risk to the public is enormous.”