On Wednesday, Cyril Ramaphosa urged South Africans to be patient while he concludes discussions with Zuma, saying he would report back to the ANC and country in the coming days.
An ANC Youth League leader close to Zuma told Sowetan: "We were only told that the [NEC] meeting has been cancelled".
On Tuesday, South Africa's parliament took the extraordinary step of postponing Thursday's state of the nation address.
After opposition pressure for a delay, the president agreed to postpone it, apparently fearing it would be disrupted by opposition lawmakers calling for his resignation.
Mr Ramaphosa, who promised to fight corruption when campaigning to be the ANC's next leader, will be its candidate in South Africa's presidential election.
Mr Zuma, 75, was replaced as party leader by Mr Ramaphosa, his 65-year-old deputy, in December. Zuma's office described a social media report that Russian President Vladimir Putin was going to visit the country this week as "fake" news.
In previous years, opposition lawmakers have shouted Mr Zuma down and been ejected from parliament by security guards in chaotic scenes. We have too many of our problems.
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At least 100 militants were killed in the Coalition's attack, a USA military official told reporters on Wednesday. The attack had left "scores of persons dead and others injured" and caused "huge damage" to the area, SANA added.
Independent political analyst Ralph Mathekga told AFP that Zuma's departure had been mishandled by the ANC.
National Assembly Speaker Baleka Mbete said on Wednesday morning that Ramaphosa would relay details of Zuma's fate later in the day. Many former supporters who have turned against Zuma have anxious that he is digging in or at least trying to make a deal, possibly including immunity from prosecution, in exchange for his resignation.
The government's Twitter accounts posted photos of Zuma sitting next to Ramaphosa - both smiling like Cheshire cats.
His presidency has been dominated by an economic slowdown, record unemployment and allegations of corruption.
He faces several court cases, including action relating to 783 payments he received allegedly linked to an arms deal before he came to power in 2009.
Zuma is also accused of helping his friends and family benefit from lucrative government contracts.
South Africa President Jacob Zuma (right) and his deputy Cyril Ramaphosa. "We can not condone or allow Zuma to escape accountability for breaking his oath of office and putting his friends and family above the best interests of the people of South Africa", the party said.