Clinton and Shevardnadze will meet next Monday.
U.S. officials appear to be leaning toward support for a UN force to replace about 2,000 Russian troops in Georgia if progress can be made in peace talks there between the government and a separatist movement.
Last Friday, talks under UN auspices in Geneva deadlocked and now will move to UN headquarters in New York on Monday.
Moscow has indicated it would welcome a peacekeeping force in Georgia, presumably wanting Russian troops to be part of such a force, U.S. officials said.
"One of the advantages of a full fledged UN peacekeeping force is to limit the ability of the Russians to exert significant influence on their borders," said another official.
The two officials spoke on condition they not be identified.
A substantial Russian presence in Georgia "offers opportunities that one would like to avoid," he said.
But Shevardnadze himself has warned against "the mentality" of Russian imperialism.
Both Shevardnadze and Abkhazian separatists have asked for a UN force to help keep peace.
U.S. humanitarian and technical assistance to Georgia has totaled $233 million over the last two fiscal years.
The officials said that the administration also wants to help ensure safe return of some 300,000 refugees, mostly ethic Georgians, driven out of the Abkhazia region of George by the separatists.
Earlier this month, Russian President Boris Yeltsin signed a treaty of friendship with Shevardnadze, pledging to rebuild Georgia's army.
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