In May, Russell said he had acquired a 82% stake in Forbes Global Media Holdings in a deal that values the company around $800 million.
"I just bought global Forbes ... You understand when you have in your hands the key to the most authoritative global brand, this key will give me access to anyone," Musaev was quoted by the newspaper as telling his associates on the tape.
In another recording, Musaev allegedly called Russell "the face" of the deal and stressed the need for his own participation to be kept secret.
However, Russell told the newspaper that Musaev had nothing to do with the deal and that any reports to the contrary were "false."
"There is not a single dollar of capital from any Chinese or Russian citizen or entity, including Musaev," Russell was quoted as saying by the newspaper.
At the same time, the US businessman refused to provide any specific information on the deal, saying he was required by law not to disclose the exact terms until the final agreement is signed, presumably in November, the report said.
Meanwhile, Forbes Russia Development Director Dmitry Ozman said that the Russian branch of the media group was not aware of the $800 million purchase deal.
"At Forbes, we do not know anything about the deal. He [Musaev] has not commented on the matter in a private conversation with me," Ozman said on Telegram.
In September 2018, Musaev announced the acquisition of the Russian edition of Forbes from Alexander Fedotov, vowing to form the publication's board of directors and invite a number of independent directors.