An investigation into the “activities” of the Muslim Brotherhood and the UK’s policy towards the group is ordered by David Cameron.
Information on the Islamist organisation is being gathered by MI5 and MI6 and from other countries, including on the scale of its operations in the UK.
The Times said the review was prompted by evidence received by the government that brotherhood leaders met in London last year to plot their response to events in Egypt.
Since the military ousting of brotherhood leader Mohammed Morsi as president in July, it has been blamed by Cairo for a campaign of violence.
The group insists it remains an entirely peaceful organisation but is accused of being behind a wave of deadly attacks on the police and military.
Responsibility for a bomb attack on a tourist bus in the Sinai peninsula which killed three South Koreans from a church group and the Egyptian driver, is also among issues being examined.
The prime minister’s review is being led by Sir John Jenkins, Britain’s ambassador to Saudi Arabia, which has also declared the brotherhood a terrorist organisation.
There is pressure from Gulf states for tougher action, with Qatar facing sanctions from neighbours over its continued support for the brotherhood.
A Downing Street spokeswoman said: “The prime minister has commissioned an internal government review into the philosophy and activities of the Muslim Brotherhood and the government’s policy towards the organisation.”
Initial work has already been carried out by National Security Adviser Sir Kim Darroch, the Times said.
It quoted officials as saying it was “possible but unlikely” the brotherhood would be added to the list of groups banned by Britain for terrorist connections.
Mr Morsi and many other senior figures are imprisoned facing trial in Egypt following the coup, which resulted in protests that killed at least 1,000.
Mass trials of his supporters – which have already resulted in hundreds of death sentences – have met with international condemnation.
The brotherhood – whose political and charitable model has been widely copied – has long had a presence in London, but there have been reports that a significant number of prominent members have fled to the city from Egypt.