The Cobra committee will consider the threat from extremist group Islamic State, which said the Briton would die unless attacks on its forces stopped reports BBC.
The video posted online purports to show the beheading of Steven Sotloff.
On Tuesday, Downing Street confirmed it was aware that IS had a UK hostage.
Officials said Mr Cameron had known about the situation for some months but no public comment had been made.
The family of the British hostage have asked the media not to release his name.
The hostage appears at the end of a video – released on Tuesday – which also shows a masked jihadi with an English accent. The footage then apparently shows the beheading of a second American captive, journalist Mr Sotloff, 31, who was captured in Syria last year.
That came two weeks after IS released a video showing the killing of another US journalist, James Foley.
The US has launched more than 120 air strikes in Iraq in the last month, in an attempt to help Kurdish forces curb the advance of IS militants.
The advance of the group, which has been accused of ethnic cleansing in the region, has seen it take control of parts of Syria and northern Iraq in recent months.
Britain has not taken military action against IS so far, but Mr Cameron refused to rule out the possibility earlier this week. He is due to set out his views in more detail during Prime Minister’s Questions later.