The proposal, part of the government's plans to replace the country's US-built Trident missile nuclear deterrent, would lead to Britain reducing its stockpile of warheads to about 150, from the 200 or so it currently has.
Without citing its sources, the tabloid said that Blair would also propose that the four Royal Navy Vanguard class submarines which carry the missiles be reduced to three when Trident is replaced.
A spokeswoman for Blair's Downing Street office declined to comment on the report when contacted by AFP.
The Sun, Britain's top selling daily newspaper, quoted an unnamed government adviser as saying: "This is not a good time to be giving up our nuclear weapons."
"Yet the PM wants to demonstrate that we want fewer so the overall number will be cut."
Anti-nuclear campaigners in Britain argue that the estimated 25 billion pounds (37 billion euros, 46 billion dollars) it could cost to replace Trident should instead be channelled into health and social care programmes as well as the fight against global warming.
Blair and the man tipped to succeed him before September next year, finance minister Gordon Brown, favour replacing Trident, with the government line that a nuclear deterrent is a key "insurance policy" in an uncertain world.
A parliamentary vote is due in the new year, but the vote is likely to be "whipped" -- where lawmakers are told to toe the party line rather than follow their consciences in a free vote.
The vote in parliament may sharply divide members of the governing Labour Party -- according to a poll published on Monday by The Independent, half of the 80 Labour members of Parliament surveyed, of the more than 350 total Labour MPs, wanted to retain the nuclear deterrent, while 39 percent did not.
Of the 52 legislators belonging to the main opposition Conservative Party who were questioned, out of 196 total Conservative legislators, 94 percent supported retaining the deterrent.
CommunicateResearch surveyed a total 156 MPs between November 13 and 29 for the poll.