United States President Barack Obama and Russian counterpart Dmitry Medvedev are expected to announce nuclear weapons cuts when they meet in Moscow on Monday.
Officials on both sides have been quoted as saying a document has been agreed, although Russia says it is not final, the BBC reports.
Mr Obama and Mr say they want significant cuts - possibly down to 1,500 warheads each. They currently have 6000 nuclear warheads each.
Russia has also been pressing Mr Obama to scrap a US plan for a missile defence shield in Europe.
Afghanistan and Iran are also on the agenda.
The presidential Air Force One plane carrying Mr and Mrs Obama landed at Moscow's Vnukovo airport on Monday morning.
Mr Obama is expected to hold talks with Vladimir Putin, currently prime minister and formerly president, on Tuesday. Many analysts say he is still in the driving seat in the Russian government.
Both sides have made clear their desire to improve, or "reset", relations between Washington and Moscow.