Prokhorov's holding group Onexim has sent a letter to Citibank, which is helping drum up candidates to buy the newspaper, Vedomosti reported, without giving official confirmation of the bid.
The paper, known for its critical take on Russia's tightly-controlled political system, is jointly owned by the Finnish media company Sanoma, Dow Jones and the Financial Times.
Citing a source who saw the letter, state news agency ITAR-TASS said the Onexim group was also interested in acquiring other Sanoma assets.
Spokespeople for Prokhorov and his group declined to comment.
Sanoma, which also declined to comment, has said it is reviewing its operations in Russia as well as Eastern and Central Europe and Belgium.
Ekaterina Ovchinnikova, a spokeswoman for Moscow-based Sanoma Independent Media, which prints the newspaper, told AFP: "As soon as the deal is completed we will release all the details."
Prokhorov, who is the owner of US basketball team the New Jersey Nets, made his fortune in banking and the metal industry. Forbes magazine estimates his wealth at USD 10.9 billion.
Vedomosti is one of the country's few remaining independent daily papers, and is known for its often blistering opinion pieces.
After Kremlin-linked oligarch Alisher Usmanov took control of Kommersant in 2006, the respected daily broadsheet significantly toned down its criticism of the authorities.
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