Leonid Nevzlin, a top shareholder, who is in exile in Israel, said they made a proposal to swap control of the company for the release of Khodorkovsky and another jailed shareholder, Platon Lebedev, a week ago, but had not got any reply.
"We are ready to do everything to obtain the freedom of our friends. If we get guarantees that they will be released, we will hand over our shares," currently worth $14.6 billion, he said.
"There can be only one guarantee - first their release and then we will stop being shareholders," added Nevzlin, who is the second-largest shareholder with an 8% stake, after Khodorkovsky's 26%.
All six main shareholders - who control their stakes via the Menatep Group holding company - are either in jail, wanted abroad or in the case of one, already sentenced to a suspended one-year jail term for tax evasion.
Nevzlin added in an interview with Moscow Echo radio that part of the deal would also have to be "a halt to the prosecution" of all the shareholders.
"We are ready to do everything to obtain the freedom of our friends"
Menatep holds a 44.1% stake in Yukos, Russia's largest oil producer, which since June has been the target of an onslaught by the Russian authorities widely believed to be provoked by Khodorkovsky's political opposition to President Vladimir Putin.
Market watchers said the offer showed the desperation of the Yukos owners, and the news sent the oil company's share price down nearly 0.5% in morning trade.
Roland Nash, oil and gas analyst at Renaissance Capital finance house, said this would mean the government acquiring control "of a privatised company through the use of the legal system to prosecute shareholders."
"If there are no other means than ransom to set hostages free, then normal people offer ransom," said the head of the Yukos-financed Open Russia charity, Alexander Osovtsov.
Khodorkovsky, Russia's richest man, was arrested at gunpoint on his company jet on 25 October and jailed pending trial on charges of massive fraud, tax evasion and embezzlement.