Susan Schwab, the US Trade Representative, said on Friday: "We have an agreement in principle and are finalising the details."
She called the deal "an important step in Russia attaining membership in the WTO".
She said she hoped to sign the agreement with German Gref, the Russian economic development, minister next week in Hanoi, at the summit of Asia-Pacific Economic Cooperation (APEC) countries.
Both George Bush, the US president, and Vladimir Putin, the Russian president, are due to attend the APEC summit in the Vietnamese capital on November 18.
"Both sides have agreed on all principal conditions for this agreement," Gref's ministry affirmed in Moscow.
"Both delegations are currently holding internal consultations in order to ensure the signing of a bilateral agreement on market access during the APEC summit in Hanoi."
Alexander Shokhin, the head of the Russian Union of Industrialists and Entrepreneurs, said on Friday: "A deal has been made.
"Presidents Vladimir Putin and George Bush should shake hands on the deal when they meet in mid-November at the Asia-Pacific Economic Cooperation [APEC] summit in Hanoi."
"It's mutually beneficial - it's in the interests of Russia because we receive the opportunity to operate in foreign markets"
Arkady Dvorkovich, the head of the Kremlin's economic staff
Sources in the Russian capital said a formal announcement was planned for later on Friday.
Accession would stimulate Russian service industries such as telecoms, banking and insurance, and "lead to a step-up in reforms by Russian companies to keep pace with the competition," said Peter Westin, chief economist at MDM-Bank in Moscow.
Agreement with the United States is key to the 149-member World Trade Organisation (WTO) accepting Russia, whose $1 trillion economy is the largest outside the trade club.
Dvorkovich said Washington and Moscow had closed the gap on key issues, and a two-way agreement would make a comprehensive WTO accession deal for Russia achievable within months.
He said: "It's mutually beneficial - it's in the interests of Russia because we receive the opportunity to operate in foreign markets, and introduce foreign countries to the Russian market on the basis of established rules."
One European diplomat said that, after a US-Russian breakthrough, wrapping up a final WTO entry deal was technically possible by next autumn - but would be politically challenging.
"All of the issues still open on the international front will have to be resolved quickly," the Moscow-based diplomat said.