The Washington Post reported that the plans outlined to President Bush by Mr Rumsfeld would probably see the emphasis on large aircraft carriers dropped and a move towards long range stealth bombers.
US officials have confirmed reports which indicated that the current review of defence policy would lead to dramatic reforms in armed forces strategy and weaponry.
The moves in strategy were discussed at a meeting at the White House earlier this week.
Cold War mindset
President Bush ordered the strategic review after making an election campaign pledge to drag the military out of a Cold War mindset towards a flexible approach.
Mr Rumsfeld has apparently accepted this new policy, though no decisions have yet been taken.
President Bush has not yet budgeted for any boost in military spending but has made it clear that new money could be made available once the review is completed.
Mr Rumsfeld is thought to have reported to the president that there should be a shift in policy from Europe to Asia, where China is seen as a growing threat compared to the decreasing danger posed by Russia.
The review is also understood to mark a shift away from the longstanding policy that the military must be able to fight two major wars in different theatres simultaneously.
Stealth favoured
Changes in strategy are likely to reduce the role of the large aircraft carriers, previously an emblem of gunboat diplomacy, but now seen as too vulnerable to missile attack.
There are plans to design smaller vessels oriented to missile defence.
The vast distances needing to be covered in Asia and the paucity of US bases could render short-range fighters less important.
There could be fewer of the new F22s and the Joint Strike Fighter, for which the UK has committed $2bn, is under review.
The favoured plane seems to be the long range B2 stealth bomber which flew from the United States to bomb Serbia during the Kosovo war.
It is believed that the growing proliferation of sophisticated missiles will mean the acquisition of ships and vehicles as well as planes with "stealth" capabilities.
President Bush is said to have agreed with the thrust of the defence secretary's report.