Former oil tycoon Mikhail Khodorkovsky and his business partner Platon Lebedev are appealing for parole after serving more than half of their sentences, the two men's website has said.
Khodorkovsky said he did not acknowledge his guilt.
Already behind bars since 2003, Khodorkovsky and Lebedev were sentenced to a further six years in prison for embezzling nearly $30bn worth of his own Yukos company's oil and laundering the proceeds in a widely condemned trial in December.
Last week, a Moscow court upheld the two men’s second conviction, but cut their sentences by a year.
Khodorkovsky's first bid for parole in 2008 was unsuccessful.
Kremlin critics have labeled Khodorkovsky's jailing part of a political vendetta by Prime Minister Vladimir Putin over the ex-Yukos head's funding of opposition parties in the early 2000s.
Putin has consistently denied any political motivation behind the convictions, saying last year that "a thief belongs in jail."
Veteran Russian human rights advocate Lyudmila Alexeyeva said Khodorkovsky's early release was unlikely.
"It would be wonderful if the court approved his appeal but I think it is unlikely that he will be released on parole," Alexeyeva told RIA Novosti on Tuesday.
She said however granting the two men parole would be a "wise" way for the Kremlin to end Russia's most politicized case.
Pavel Krasheninnikov, the chairman of the Russian parliamentary committee for legal affairs, also said he believed the bid for early release would fall through.
The European Court of Human Rights is expected to deliver a ruling later on Tuesday on whether the two men’s rights were violated after their arrest.
Last week, the London-based rights group Amnesty International recognized Khodorkovsky and Lebedev as prisoners of conscience.
When asked in a news conference on May 18 whether Khodorkovsky would be a danger to society if released, President Dmitry Medvedev said: "No danger whatsoever."
MOSCOW, May 30 (RIA Novosti)