State Department officials could not immediately confirm the report which said the two sides agreed to lower the ceiling for deployed nuclear weapons from the 2,200 decided on in 1991 to between 1,500 and 1,675.
It would mark a breakthrough in months of negotiations to replace the Strategic Arms Reduction Treaty (START), which led to deep cuts in both nuclear arsenals after it was signed in 1991 before the collapse of the Soviet Union.
The Wall Street Journal, citing administration and arms control officials, said US and Russian arms control negotiators reached an "agreement in principle" on the nuclear arms reduction pact.
It said that the deal, in addition to reducing deployed nuclear weapons, would lower nuclear delivery systems more sharply to between 700 and 800 a side.
The breakthrough in the negotiations came two weeks ago when National Security Adviser James Jones and Admiral Michael Mullen, the chairman of the joint chiefs of staff, went to Moscow to overcome stumbling blocks, it said.
Those involved two issues on verification, sharing information on missile flight tests and inspections at missile production plants, it said.
The Wall Street Journal said the agreement was approved in principle last week during a telephone conversation between US President Barack Obama and Russian President Dmitry Medvedev.
Question arose as to whether the START talks were in trouble after negotiators missed a December 5 deadline.
Nor was there a deal by January 1, even though Obama's White House said on December 17 that it still aimed to "conclude a good and verifiable (START) agreement by the end of the year."
However, analysts said negotiators were under pressure to clinch a pact in the run-up to a May review conference for the Nuclear non-Proliferation Treaty (NPT), which obliges the nuclear powers to show progress on disarmament.