Even as the Ukrainian government moves to re-privatize the mill, courts are continuing to mull legal challenges to the step that came before -- Kryvorizhstal's re-nationalization.
Courts had already ruled in favor of a decision to nullify the mill's first sale to private owners. But the Supreme Commercial Court is currently considering an appeal.
Serhiy Vlasenko, a lawyer representing Kryvorizhstal's former owners, told RFE/RL the government is being too hasty in putting the mill on the auction block.
"I don't agree with the government that all the legal matters are finished, Vlasenko said. "The legal matters are far from being finished. The Ukrainian prime minister allows herself to make a declaration [on privatization] as if knowing what decision the Supreme Commercial Court will make. I personally have no idea what decision the Supreme Commercial Court will make."
In addition, Vlasenko said a Ukrainian Supreme Court decision in late December upholding the legality of the first privatization has yet to be annulled.
He says the government should wait for all legal matters to be concluded before they take any further steps toward privatization.
Kryvorizhstal's controversial first sale took place last year.
Rinat Akhmetov, considered one of the wealthiest businessmen in the Donetsk region, paired up with Vikor Pinchuk, the son-in-law of former President Leonid Kuchma, and purchased the mill for $800 million.
The government says the sum was significantly lower than those offered by other bidders.
Viktor Yushchenko and other leading figures of last year's Orange Revolution pledged to investigate shady privatization deals. One of the new administration's first steps was to re-nationalize Kryvorizhstal earlier this month.
But some outside observers aren't be impressed.
Stuart Hensel of the London-based Economist Intelligence Unit, says Kryvorizhstal is not a success story for the Yushchenko administration:
"I think the obvious thing about this is that the government has handled this very badly," Hensel told RFE/RL. "I think it's taken far longer than anyone expected. The government has proved far less able to send out a coherent, timely message about what its intentions are regarding re-privatization. And this has turned out to be a major distraction for the government, and a significant source of concern for potential investors."
The government has so far failed to specify which pre-Yushchenko privatization deals it intends to investigate. This uncertainty has left many potential investors nervous. In the end, Hensel says, the Kryvorizhstal affair may backfire:
"I think [the government], unfortunately, hasn't gone about it in a very good way," Hensel said. "So that even though putting Kryvorizhstal back in private hands will boost budget revenues and will be seen by many as increasing social justice, I think the government has created as many problems as it is solving by going about it in the way that it has."
But Volodymyr Horbach of the Kyiv-based Institute of Euro-Atlantic Cooperation says the government has no choice but to look into dubious privatization deals from the past.
Ukrainians supported Yushchenko and Tymoshenko precisely because they pledged to instill a sense of justice, Horbach said. A majority of the public was in favor of the mill's re-nationalization.
"The public thinks that it is normal to return the property back to the state," Horbach said. "They see it as an objective and fair process."
Horbach says that with parliamentary elections due next year, many politicians are keen to stay on good terms with their electorate, and therefore may back more re-nationalization plans.
But would Kryvorizhstal's re-privatization prove an equally popular move?
Horbach says no. After a decade of rampant corruption and nepotism, he says, most Ukrainians feel a deep distrust for private business.
A recent poll by the Ukrainian Institute of Economics indicated that only 20 percent of Ukrainians support privatization. A majority of respondents said they would prefer to work in a state-owned company.