Gordon Brown will make the offer at a meeting of the UN Security Council to stop the spread of nuclear weapons and reduce existing stockpiles.
The proposed cuts were in line with government efforts to find ways to reduce the huge deficit in public finances.
But the Prime Minister said that keeping Britain's nuclear deterrent "not negotiable".
At UN meeting, Mr Brown will ask all countries to come together to achieve long-term ambition of creating a nuclear-free world.
He will say: "If we are serious about a world free of nuclear ambitions we will need statesmanship, not approaching danger."
Liberal Democrat leader Nick Clegg welcomed the proposal, saying it is an important development.
He told the BBC: "I really welcome the proposal that kicked off like this"
"It's unrealistic for us to believe that we can provide £ 100 billion cost of a replacement for the Trident for 25 years.
"I think the strategic context in which the decision was a very different place as well, we do not face the threat of the Cold War in the same way as we advance."
The government has announced that it has cut supplies from 200 to 160 British Trident warheads, and many Labour MPs want the government to spend the entire weapon.
Officials traveling with the prime minister warned that reducing the number of submarines from four to three would not result in costs that is proportional cuts of 25%, because more must be spent to maintain the whole.
Earlier, Defence Minister Bob Ainsworth said the future of Trident not included in the review when lawmakers support reforms in 2007, but he suggested during the interview Sky News that the cost of the project is reviewed.
The Conservatives support the Trident, but said it will form part of a review of the overall defense budget they plan immediately if they win the next election.
Liberal Democrats have called for a defense of smaller, cheaper to reflect the changing nature of the weapons of war and the threat to Britain.
Liberal Democrats argued that Britain can not afford to replace the Trident replacement are equivalent when the pelayananya ended in 2024.
A report by the think tank Reform, which was published on Tuesday, argues that not renew Trident could save £ 70bn over 25 years.
£ 40bn more could be trimmed from the defense budget by removing some of the hardware and reduce waste, he added.
In the upcoming UN meeting, U.S. President Barack Obama who will lead the meeting of the Security Council on Thursday as part of the process of preparing a substitute for the Non-Proliferation Treaty, designed to stop countries to develop nuclear weapons.
Obama said he would try to negotiate with Moscow to reduce U.S. nuclear warheads and Russia, which make up 95% of the world total, from each of the 2000 to 1500.
But the most pressing issues for leaders at the meeting was to be how to stop the further spread of weapons to countries that non-nuclear.