The ANC's national executive committee (NEC) extended its scheduled meeting into a third day on Monday, after Tourism Minister Derek Hanekom proposed the motion of no-confidence on Saturday, said Beeld, an Afrikaans-language daily.
Committee members were locked in a "fiery and fierce" debate over whether a secret ballot should be used to decide the no-confidence motion, it added, citing unnamed sources who had attended the meeting, Reuters reported.
The ruling party's spokesman did not respond to a telephone call to seek comment. In a statement on Sunday, the ANC did not give a reason for the extension of the meeting.
The committee, 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 5-yearly congress.
Zuma's presidency has been plagued by scandal 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.