Lagarde has emerged as the odds-on favorite for the job. Her appointment would make her the first woman in charge of the scandal-rocked fund but may also increase tensions with developing nations that argue countries outside of Europe should be allowed to lead the organization.
Brazilian officials have not spoken out in favor or against Lagarde's candidacy. But they previously have emphasized that the IMF's next leader should be chosen on merits, not based on geography.
The IMF is hunting for a new leader to replace former managing director Dominique Strauss-Kahn, of France, who quit May 18 after he was accused of attempting to rape a New York hotel maid. He has denied the allegations.
Lagarde will meet with the head of Brazil's Central Bank and also the nation's finance minister, Guido Mantega. In recent years, Mantega has loudly fought for reforms in the IMF, World Bank and other multilateral institutions that would take into account the growth of emerging nations such as Brazil, China and India.
"We must establish meritocracy, so that the person leading the IMF is selected for their merits and not for being European," Mantega said earlier this month. "You can have a competent European ... but you can have a representative from an emerging nation who is competent as well."
Mantega also has said that whoever is chosen to replace Strauss-Kahn should only hold the job until Strauss-Kahn's term expires at the end of 2012. That, Mantega has argued, would give IMF member nations more time to carefully choose a full-term chief.
China has suggested it is time to shake things up at the IMF, with Foreign Ministry spokeswoman Jiang Yu saying the leadership "should be based on fairness, transparency and merit."
South African Finance Minister Pravin Gordhan spoke in stronger terms earlier this month.
He said the new director should come from an emerging economy, to "bring a new perspective that will ensure that the interests of all countries, both developed and developing, are fully reflected in the operations and policies of the IMF."
French Embassy spokesman Stephane Schorderet said Lagarde will return to Paris on Monday night and plans to stump for the IMF job in China next week.
She also plans to visit other influential developing nations to convince them that if given the job, she will not exclusively focus on Europe, where the fund is closely involved in a half-dozen bailout deals.
According to France's foreign minister, Lagarde has already won the backing of the Group of Eight rich nations. Interviewed Sunday on French television channel Canal+, Alain Juppe said there was unanimous support for Lagarde among the eight leaders at their annual summit in Deauville, France, last week.
The U.S., whose vote will be crucial for Lagarde's nomination, has not officially endorsed a candidate.