The National Executive Committee (NEC), the party's highest decision-making body, is expected to finalize the issue on Tuesday and brief the nation on its decision, after marathon meetings that continued into late Monday night.
Legal experts said that although Zuma was technically fired, the NEC cannot fire him. If Zuma digs in and refuses to be fired, he has to be removed through a parliamentary motion.
Should Zuma fail to resign, the NEC will have to decide whether to bring a motion of no confidence in Zuma to the parliament, said a legal expert who spoke on condition of anonymity.
As pressure for Zuma to step down mounts, opposition parties have called for the dissolution of the parliament.
Earlier in the day, speculation was rife that Zuma demanded a three- month "notice period," after which he will resign unconditionally. However, that proposal was shot down by NEC members.
Zuma, who became South African president in 2009, has been involved in scandals.
Deputy President Cyril Ramaphosa, who took over the ANC leadership in December in a hotly contested election, promised to get rid of corruption and turn around the country's economy.