France's top appeals court will rule on Lagarde's challenge to a December court ruling that she be tried for negligence in the affair, which ended with Tapie walking away with 404 million euros (USD 445 million) in taxpayer money.
If the court orders a trial, the 60-year-old will go before a special tribunal that hears cases against government ministers accused of wrongdoing in the discharge of their duties.
Lagarde's involvement in the case stems from her decision to let the row be settled by arbitration instead of the courts, which would likely have resulted in a much smaller settlement for Tapie.
The negligence charge relates to that decision and Lagarde's later failure to challenge the award, which was hugely prejudicial to the state.
More From This Section
A court has since found the arbitration to be fraudulent because one of the arbitrators had links to 73-year-old Tapie.
She herself is not accused of personally profiting in any way.
"I've always acted in accordance with the law, and I've always had in mind the public interest," she told AFP in an interview in Washington earlier this month.
"It was not my duty to select the arbitration panel, to investigate their past and history, and I had no reason to doubt their probity and honesty," she said.
Investigating magistrates however found evidence of "serious negligence on the part of a minister tasked with conducting affairs of state" and in December ordered the case go to trial.
A high-profile trial in Paris would be a blow to the IMF boss, who embarked on a second term as head of the international lender in July.
If tried and convicted, she risks up to a year in prison and a fine of 15,000 euros.
Lagarde replaced fellow French compatriot Dominique Strauss-Kahn as managing director of the IMF in July 2011. He had resigned his post two months earlier to fight sexual assault allegations.