State broadcaster SABC reported on Monday that Mr Zuma, 75, had agreed to step down as head of state, with correspondent Tshepo Ikaneng citing "authoritative sources".
The subsequent rebuttal from the President's spokesman caused the rand, which had risen as much 1% on the news of his alleged departure, to lose ground.
Sky News' Africa Correspondent, John Sparks, said the ANC's wrangling over Mr Zuma's future "could split the party".
"The stakes really are that high," he added, noting that Mr Zuma "clearly does not want to go".
The meeting of the ANC's national executive committee (NEC) at a hotel in Pretoria is thought to be split between those keen to allow Mr Zuma to complete his time in office, and others who would like to see a quick transfer of power to deputy president Cyril Ramaphosa.
On Sunday, Mr Ramaphosa, 65, told a party rally in Cape Town: "We know you want closure...because our people want this matter to be finalised, the NEC will be doing precisely that."
:: ANC considers Zuma's future amid protests in Johannesburg
But John Sparks, who is in Pretoria, said the meeting had been going on for many hours, suggesting "real division, real debate", adding that Mr Zuma had "pockets of support in that meeting".
Nevertheless, he said it is "generally thought in South Africa that the NEC want to get rid of Jacob Zuma".
Since coming to power in 2009, Mr Zuma has been dogged by allegations of corruption.
The 107-member NEC could "recall" him - essentially ordering him to stand down, although he would be under no constitutional duty to obey.
A vote of no confidence would then be held in Parliament.
South Africa is set to hold a presidential election next year. Mr Zuma has not publicly indicated whether he is prepared to step down voluntarily.