The former Yukos boss is currently in a Siberian prison camp
Lawyers acting for former Yukos chief executive Mikhail Khodorkovsky have requested his early release.
Mr Khodorkovsky, Russia's richest man when arrested in 2003, was found guilty of tax evasion in 2005.
He is currently half-way through an eight-year sentence in a case critics of the Kremlin have said was politically motivated.
Mr Khodorkovsky, who insists he is innocent, is entitled to request parole at this stage in the prison sentence.
"Khodorkovsky's defence today asked that he be released on parole," his lawyer Yury Schmidt told reporters.
Mr Schmidt said Mr Khodorkovsky hoped that he had a better chance of succeeding under the newly inaugurated Russian President Dmitry Medvedev than his predecessor, Vladimir Putin.
"We have much hope in the words of Medvedev on the independence of the judiciary," Mr Schmidt said.
There has been speculation that Mr Khodorkovsky would turn down a presidential pardon, as accepting it would mean having to admit guilt over charges that he has always denied.
The head of the prison service in the eastern Siberian town of Chita, where Mr Khodorkovsky is imprisoned, said he thought it unlikely that his bid for parole would be successful.
"To be granted parole, people need to work, to behave well, not to violate the rules," Yunus Amayev is reported as saying, according to the Interfax news agency.
Mr Khodorkovsky was reported to have violated prison rules four times last year, according to the head of the Russian prison service.
At the beginning of the month, fresh charges were laid against Mr Khodorkovsky by Russian prosecutors, who accused him of misappropriating 350 million tonnes of oil and laundering billions of US dollars.
The charges, dismissed as absurd by his lawyers, dampened hopes that the Kremlin may have been planning to pardon him.
Yukos, once Russia's biggest oil company, was declared bankrupt in 2006 and ceased to exist as a legal entity in November 2007.