The U.S. nuclear stockpile might be trimmed to as low as 300 warheads under one such proposal, an unnamed U.S. official told the newspaper.

Other proposals would see the U.S. arsenal cut to between 1,100 and 1,000, and between 800 and 700, the official said.

The U.S. currently has 1,790 warheads.

The cut would not be unilateral but could be negotiated with Russia in future arms reduction talks.

Under the New Start nuclear arms treaty which came into effect in February last year, the U.S. and Russia must reduce its nuclear arsenals to 1,550 warheads.

The new proposals, confirmed by the Pentagon on Tuesday, have not been presented to President Barack Obama yet.

The prospect of new nuclear cuts is certain to become a hotly debated issue during the presidential campaign, the Wall Street Journal said. New Start was opposed by many republicans in the U.S. Senate and was also criticized by leading presidential contenders Mitt Romney and Newt Gingrich.

Last month, Obama and Defense Secretary Leon Panetta unveiled a revamped national military strategy, which hinted at possible steep reductions in the U.S. strategic arsenal.

The document, presented at the Pentagon, said: “It is possible that our deterrence goals can be achieved with a smaller nuclear force.”

However, the Pentagon’s 2013 spending plan, presented on Monday, did not propose any nuclear cuts.