Even if Prime Minister Manuel Valls signs the decree for the extradition of Yoo Som-Na over the catastrophe that killed more than 300 people, the decision can still be contested in France's highest administrative court.
A lawyer for Yoo said extradition would be "unjust" and that her legal team would continue to fight.
"We're not going to stop there, certainly not," Herve Temime told AFP.
Yoo, who was detained in Paris in May 2014, is wanted in South Korea on suspicion that she embezzled millions of dollars from subsidiaries of her family's company, Chonghaejin Marine Co.
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Yoo strongly denies the accusations.
Her father Yoo Byung-Eun had been the target of a massive manhunt in South Korea after he refused to respond to an official summons following the ferry disaster.
The tycoon, who in addition to his substantial business interests also ran a religious group, was found dead in a plum orchard two months after the disaster.
An autopsy on his badly decomposed body failed to determine the cause of death.