"It certainly would be good news if it came about," Mr Christopher said to reporters here as Russian and Chechen officials met in Moscow to try to thrash out the details.
Mr Christopher earlier said he would urge the Russians "in the strongest way" to stop the onslaught in Chechnya.
He and Mr Kozyrev were due to meet over dinner and for a full day session today. The talks are also expected to focus on Russian worries about Nato's future role, US fears about threats to Russian democratic reforms, and differences over Bosnia.
US officials said Mr Christopher and Mr Kozyrev would discuss an invitation for President Bill Clinton to meet President Boris Yeltsin in Moscow in May - coinciding with 50th anniversary celebrations of the allies' victory over Germany in the Second World War.
Washington has been critical of the Russian bombardments, but does not back the rebels, fearing a chaotic process of disintegration in Russia.
When he left Washington on Monday, Mr Christopher urged Chechen rebels to respond positively to any Moscow peace overtures. He has said there are no plans to scale back US aid because of Chechnya, but has emphasised that Mr Yeltsin must get Russia back on the reformist track.