According to 'The Times', military units in the UK remain on standby at their bases and would be moved by helicopter in an emergency.
A government source told the newspaper that the requirement was to "take swift action to neutralise terrorists, rather than to cordon and negotiate".
It is believed that the Bataclan concert hall massacre in Paris, in which 89 people were killed on Friday night, has convinced British security chiefs to switch their strategy from seeking to negotiate with gunmen.
The so-called Islamic State (ISIS) has claimed it was behind the killings.
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The report comes against the backdrop of the G20 summit at Antalya in Turkey where world leaders have agreed to do more to share intelligence and cut off funding for terrorists.
"Here at this summit, we have agreed to take further important steps... To cut off the financing that terrorists rely upon, to counter the extremist ideology and the terrorists' propaganda and to better protect ourselves from the threat of foreign fighters, by sharing intelligence and stopping them from travelling.
He met Russia's President Vladimir Putin to discuss tackling the ISIS group and the Syrian war.
He said the gap between Russia and the West's position on Syria "has been enormous", but now "everyone recognises the need for compromise".
Cameron also reiterated he would not ask British Parliament to vote on extending British military action into Syria until there is enough support.
"I need to build the argument, I need to take it to Parliament, I need to convince more people," he said.