Acknowledging that the party faithfuls want to see a change, ANC president Cyril Ramaphosa told a crowd in Cape Town on Sunday: "As you have all heard, the National Executive Committee of the ANC will be meeting tomorrow. and because our people want this matter to be finalised, the NEC will be doing precisely that".
"We know you want closure on this matter", Mr Ramaphosa said to the crowd, "but it is important to manage these discussions with goal".
The 75-year-old Zuma, in power since 2009 and mired in corruption allegations, has been living on borrowed time since Ramaphosa took over his other role as leader of the ruling party in December.
In this episode, The Stream hosts a panel of South African commentators to explore President Zuma's legacy and the future of the country's political landscape.
Zuma survived calls a year ago by some members of the NEC for him to quit.
"I don't understand why the ANC's new leadership has not removed Zuma already because that is long overdue", he said at the rally.
Down but not out- yet South Africa's embattled President Jacob Zuma has rejected a party request that he resign
Their meeting is set to begin at 2pm, when the African National Congress (ANC)'s national executive committee is also due to start its special meeting in Pretoria.
The stalemate over Zuma's departure has left Africa's most developed economy in limbo, with a series of public events cancelled last week, including Thursday's State of the Nation address to Parliament. "We know that Nelson Mandela would have been against the capturing of the institutions of our country".
Ramaphosa, who only just won a bitterly fought internal election to become president of the ANC, has the support of only just over half the members of its top decision-making body. In addition, he acknowledged the former liberation movement was struggling with internal unity, but insisted Mr Mandela's centenary year "offers us a new beginning".
Local media reported that Zuma's potentially ruinous legal fees from prolonged court battles against multiple criminal charges were a key sticking point in the negotiations.
St George's Cathedral was at the forefront of the anti-apartheid struggle and during a Christmas mass service previous year its archbishop, Thabo Makgoba, called on the new ANC leadership to act "quickly and decisively" to replace Zuma as head of state. "They need to close this thing early this week".
In 2008, shortly after taking the party's helm, Zuma engineered the ousting of Thabo Mbeki from the presidency.