He has survived several parliamentary votes but this is the first time the ANC will formally discuss his position.
The top ANC body has extended its meeting to debate the motion, tabled by Tourism Minister Derek Hanekom.
Mr. Zuma has increasingly come under criticism over corruption allegations, with a recent report highlighting his links with the wealthy Gupta family.
At least two other cabinet ministers are understood to be backing Mr. Hanekom’s proposal – Health Minister Aaron Motsoaledi and Public Works Minister Thulas Nxesi.
The BBC’s Karen Allen in Johannesburg says this could shape into the toughest battle of Zuma’s career.
Earlier this month, an investigation by the country’s anti-corruption watchdog said a judicial inquiry should be set up to further investigate allegations of criminal activity in Mr. Zuma’s government.
The investigation found evidence that the Guptas, a business family with links to Mr. Zuma, may have wielded undue political influence over the appointment of ministers.
Both Mr. Zuma and the Guptas have denied any wrongdoing.
The stage has been set, President Jacob Zuma is in a battle for his political life.
In one of the first real pushes within the ruling African National Congress (ANC), top party officials are now officially debating the president’s removal.
More than 80 National Executive Committee (NEC) members have been at loggerheads in a closed meeting in the capital Pretoria since the weekend.
While Mr. Zuma is believed to still have a lot of support within the party, some ministers are calling for a secret vote on the matter, hoping this would help people within the party to vote freely.