The National Executive Committee (NEC) is likely to ask him to step down, says BBC Africa correspondent Andrew Harding.
ANC president Cyril Ramaphosa acknowledged on Sunday that the issue was causing "disunity and discord".
Mr Zuma, 75, faces a number of corruption charges after nine years in power.
There are more than a hundred members of the NEC, and many may want to share their views during the meeting in Pretoria - meaning it could be some hours before a decision is made.
What did Mr Ramaphosa say?
"We know you want closure," Mr Ramaphosa told a crowd, which had gathered to mark 100 years since the birth of the country's first black president, Nelson Mandela.
He told the crowd in Cape Town on Sunday that "our people want this matter to be finalised" and that the African National Congress (ANC) would comply.
He acknowledged the ANC was suffering "a period of difficulty, disunity and discord", and said he wanted to replace it with "a new beginning".
He pledged to tackle the corruption that has marred Mr Zuma's time in office.
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