After a debate within the administration lasting several months, it has been decided to declassify the numbers. The move would be seen as an attempt to encourage openness from other states by demonstrating America's progress in reducing its Cold War nuclear arsenal.
The announcement could be made as early as Monday when Hillary Clinton, the Secretary of State, speaks at the UN meeting to review the progress of the Nuclear Non-Proliferation Treaty, according to The Washington Post.
Arms-control groups estimate the US nuclear arsenal contains 9,000 weapons, roughly 5,000 of them active and the rest in line for disassembly.
The announcement could be timed to prevent Mahmoud Ahmadinejad, the Iranian president, from hijacking the conference with demands for more global controls of nuclear stockpiles. He speaks before Mrs Clinton.
The international community believes Iran is secretly preparing to build a nuclear weapon.
Speaking on NBC's Meet the Press, Mrs Clinton said: "If Iran is coming to say we're willing to abide by the Nonproliferation Treaty, that would be very welcome news.
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"I have a feeling that's not what they're coming to do. I think they're coming to try to divert attention and confuse the issue."
Barack Obama's staff have also reportedly held talks with Egypt over a plan to make the Middle East a nuclear-free zone, as part of the effort to block the Iranian nuclear programme.
The US had also discussed the proposal with the Arab League and other members of the Non-Aligned Movement, according to reports.
However US officials recognize that progress in the nuclear-free zone talks would not happen without first achieving major advances in Arab-Israeli peace talks.
The latest initiative could raise new tensions between Mr Obama and Israeli Prime Minister Benjamin Netanyahu. Israel has never publicly acknowledged having nuclear weapons, maintaining a policy of deliberate ambiguity since it inaugurated its Dimona nuclear reactor in 1965.
It is not a party to the NPT, which requires international inspections.