It dumped him as party leader in December, narrowly electing Ramaphosa, a millionaire former union leader, over Zuma's preferred successor, his ex-wife Nkosazana Dlamini-Zuma.
On top of this, Mr Zuma is still very popular, particularly in rural areas and his home region of KwaZulu-Natal. "He told them he was not going anywhere as he did nothing wrong", an unnamed ANC committee member told the Mail and Guardian newspaper.
Magashule said Zuma asked for three to six months to complete the job, but said the party felt that was too long, given his sinking approval ratings as critical elections approach next year.
The ANC is expected to address the media later Tuesday.
ANC officials were not reachable Tuesday, but the party called a press conference for 2:00 pm (1200 GMT) at its headquarters in Johannesburg.More news: Pochettino full of confidence after Tottenham "dominate" Juventus in Champions League
It will be very hard for Zuma to resist a formal request to step down but he would not be legally obliged to do so and could technically carry on as President despite losing the faith of his party, the BBC said.
He will then likely be ousted via a parliamentary vote of no-confidence within days.
The ANC could "recall" Zuma, which would pressure him to resign before his term ends next year.
The impasse has plunged South Africa - the continent's most developed economy - into confusion over who is running the country, with major national events cancelled amid the uncertainty.
Mr Ramaphosa, 65, said on Sunday the meeting was expected to "finalise" the situation.
"We know you want closure..."More news: Margie's Money Saver: National Pizza Day deals
In the past, the ANC had called it the "worst form of betrayal" of the party if its MPs voted with the opposition.
But Mr Zuma - who has refused to resign - would be under no constitutional obligation to obey the order.
The leadership of the ruling African National Congress (ANC) will decide today whether South African President Jacob Zuma will leave the government, at the conclusion of a negotiation process for power transition that started last week.
"We haven't given him any deadline to respond (but) when we recall our (president), we expect (him) to do what the organization expects him to do".
The party faces a tricky general election next year.
"Ultimately ... anybody who wants to lead ... the people of South Africa must have a mandate from the people of South Africa".More news: Duterte orders military to cancel helicopter deal with Canada
The NEC meeting in a Pretoria hotel had all the ingredients for a showdown between Zuma stalwarts and those backing a swift transfer of power to deputy state president Mr Ramaphosa. The budget speech, scheduled for February 21 will go ahead.
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