Details are to be hammered out by the two nations' foreign ministers during a meeting in Geneva on Tuesday and Wednesday.
Itar-Tass quoted an unnamed diplomat Monday as saying that the summit is planned for May.
"There is an invitation and it is the intention of President Clinton to come to Moscow at that time," the diplomat said.
It will be the fourth summit between the two leaders since Clinton became president two years ago.
Although Yeltsin's press office and the Foreign Ministry were unable to confirm immediately that the visit was set, White House spokesman Michael McCurry said in Washington that plans were in the works.
The trip will be on the agenda between U.S. Secretary of State Warren Christopher and Foreign Minister Andrei Kozyrev, he said.
"There will likely be a conversation about that between Christopher and Kozyrev in Geneva," McCurry said.
The topics of Yeltsin and Clinton's conversation is less clear.
The diplomat quoted by Tass said Russia was prepared to discuss Chechnya, but only its humanitarian and human rights aspects.
Russia would not, he said, discuss how to settle the issue.
"Settlement," the diplomat said, "is our own affair, and we will resolve it in keeping with our constitutional procedures."
Moscow has objected to Washington's criticism over Russian military attacks in Chechnya in recent days, although the Clinton administration has always stated that Chechnya is an internal Russian affair and that the United States supports the integrity of the Russian Federation's borders.
The two presidents are also likely to discuss European security.
Washington and Moscow are sharply divided on the expansion of NATO into the countries of the former Soviet bloc.
The two countries are also divided on their approach to the war in Bosnia.
When those differences were exposed at a recent European security summit meeting in Budapest, relations between the United States and Russia soured.
A visit to Moscow by U.S. Vice President Al Gore helped smooth things over.
But Chechnya again destabilized mutual understanding between the two nations.
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