Mr. Obama discussed the issue with Russian President Dmitri Medvedev in a private meeting Friday while both were attending the Copenhagen climate conference.
Mr. Medvedev said some work is still needed on the technical details.
Delegates from both countries have also been holding negotiations on the treaty in Geneva, Switzerland.
U.S. and Russian negotiators have been trying for months to work out an agreement to replace the 1991 Strategic Arms Reduction Treaty, START, which expired earlier this month.
Russian Foreign Minister Sergei Lavrov called on Thursday for Washington to accept deeper reductions to its nuclear arsenal and less intrusive verification measures than those in the current treaty.
But the United States says it wants to continue transparency and verification measures on Russia's nuclear arsenals.
Mr. Obama and Mr. Medvedev agreed during talks in Moscow in July that the new treaty would reduce each country's nuclear arsenal from current levels to between 1,500 and 1,675 "operationally deployed" warheads, within seven years.
Some information for this report was provided by AP, AFP and Reuters.