Sport Minister George Hilton's job has been under threat since his party, the Brazilian Republican Party (PRB), quit President Dilma Rousseff's embattled coalition a week ago.
It is "very likely" that Hilton will have to resign, a cabinet source told AFP on condition of anonymity.
Hilton was a no-show on Tuesday at a scheduled meeting on the Olympic planning process in Rio.
The PRB abandoned the ruling coalition after huge anti-government protests by Brazilians outraged over an explosive corruption scandal at state oil company Petrobras and a deep recession.
But Rousseff's chief of staff, Jaques Wagner, said yesterday that the PROS is not entitled to ministerial positions under the coalition deal.
Wagner said, he did not have "definitive information" on Hilton's departure, but that if he quit, "it would be opportune to give the ministry to Ricardo Leyser, of the PC do B (the Communist Party of Brazil), who has been following the whole process of the Olympics from the beginning."
Leyser is currently secretary of state for high-level sport. He is considered the government's point man on organising the Olympics, which open in Rio on August 5.
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