Foreign Secretary Jack Straw has failed to confirm or deny a report that a new UK nuclear weapons system is already being secretly developed.
Trident will be decommissioned in about 20 years' time
Asked about the report in the Sunday Times about Trident's replacement, he said: "We are giving consideration to the development of a new system."
Plans to replace Trident, which some estimate will cost £20bn, are expected to be drawn up by the next election.
Mr Blair has promised MPs the "fullest possible" debate before any decision.
The Sunday Times reported that an anonymous senior British source has said that work on the weapon has been underway since Mr Blair was re-elected last May.
According to the paper, the research is being carried out at the Atomic Weapons Establishment at Aldermaston, Berkshire.
The report says scientists wanted to produce a warhead using proven components to avoid breaching a ban on nuclear testing.
Mr Straw said the UK was "entitled to have a nuclear weapons system", and had reduced the numbers of systems it had from three to one.
'Fullest possible" debate
Asked if a successor to Trident was already being developed, Mr Straw said: "There is a discussion about whether we do."
The prime minister's official spokesman later said: "We are in a process of thinking about thinking about it," but added, "not this month and not next month".
Last month Mr Blair told a committee of senior MPs there would be the "fullest possible" debate on any decision to develop a new nuclear warhead.
But, he added: "I'm not committing myself to a vote... not ruling it out either."
He said Parliament tended to find a way to have a vote on big issues, and said a decision such as this was "not going to just pop out one day".
But he did say that by the end of the year "we should have a clear idea of the timeline" for a debate on replacing Trident.
Defence Secretary John Reid said last year that no decision on replacing Trident had been taken.
But he said Labour was committed to keeping Britain's nuclear deterrent.
Trident is expected to be decommissioned in about 20 years' time. The nuclear deterrent system was last updated in 1980.
Last year, a group of writers, led by Nobel Prize winner Harold Pinter, wrote an open letter to MPs saying there was "no legitimate political, military or moral reason" for replacing Trident.