Reports say that at least three of his cabinet ministers have turned against him.
Zuma has survived several parliamentary votes but this is the first time the ANC will formally discuss his position.
The top ANC body extended its scheduled weekend meeting to debate the motion, tabled by Tourism Minister Derek Hanekom.
The NEC, which is meeting in the capital, Pretoria, is the only body in the ruling party that can remove the leader of the party, besides its five-yearly congress.
Zuma himself is one of the committee’s 104 members, most of which were elected alongside the president in 2012.
Zuma’s presidency has been plagued by scandals and the nation’s anti-graft watchdog this month asked for a judge to investigate alleged influence-peddling by a wealthy family Zuma has called his friends.
Zuma has denied any wrongdoing.