The prime minister's helicopter was forced to make an emergency diversion during a trip to see troops in the southern province of Helmand in June after it was suspected insurgents had gained knowledge of the trip.
Two conversations were intercepted by NATO intelligence services in which the Taliban were understood to be plotting an attack on a VIP called the Big Commander, the Times said.
The incident deepened concern about the increasingly sophisticated nature of the insurgents' intelligence operation, the newspaper added.
No shots were fired and Downing Street played it down, but one Whitehall source was quoted as suggesting the threat was much closer than anyone said at the time.
Without quoting further military figures, the newspaper said options understood to be under consideration were media blackouts until the prime minister had left a war zone.
This is already common practice and a similar measure was imposed on Defence Secretary Liam Fox during his visit to the country this month.
Other measures included the prime minister and other senior figures only visiting the capital after a trip to Helmand.
Downing Street and the Ministry of Defence said they would never comment on the prime minister's security arrangements.
Cameron had planned to travel by helicopter from Camp Bastion to Shahzad patrol base after a televised press conference with Afghan President Hamid Karzai in Kabul.
It was his first visit as prime minister to troops in Afghanistan after the election in May.
His Chinook helicopter was forced to divert to British brigade headquarters at Lashkar Gah at the last minute after the Taliban were believed to have pinpointed which of the two helicopters he was travelling in.
(Writing by Avril Ormsby; Editing by Steve Addison)