African National Congress (ANC) party officials met with Zuma over the weekend to request his resignation, but he refused, triggering a week of dramatic political manoeuvering.
The embattled president has remained defiant in the face of pressure to resign according to party MPs quoted by several local media outlets.
On Thursday, the ANC said it was awaiting the "imminent conclusion" of negotiations between Zuma and his deputy Cyril Ramaphosa, the president-in-waiting.
The sudden decision by the party's "Top Six" leadership to abandon plans to join celebrations in Cape Town marking the 100th anniversary of Nelson Mandela's birth has prompted speculation they will join efforts to ease out Zuma.
More From This Section
Local media said Ramaphosa and Zuma would meet in the capital Pretoria on Friday while analysts speculated that the party's top brass had been drafted in to heighten pressure on him to go.
The government also postponed an awards ceremony scheduled for Saturday at which Zuma was to officiate, effectively emptying the president's short-term diary.
A pro-Zuma newspaper suggested on Friday that the president's fate was close to being sealed.
The New Age daily said Zuma would gather his family at his official residence in Pretoria this weekend to inform them of his decision to step down.
Zuma, 75, who has been in office since 2009, has clung to power despite a string of corruption scandals, an economic slowdown and record unemployment.
He faces several court cases, including action relating to 783 payments he allegedly received which were said to be linked to an arms deal before he came to power.
Many of the recent graft allegations are linked to the Guptas, a wealthy Indian business family accused of improperly winning government contracts and influencing cabinet appointments.
"The ANC have been pushed into the corner and so have to act and take a decisive decision," political analyst Ralph Mathekga told AFP.
"I think they might be announcing something over the weekend."
Ramaphosa, a seasoned negotiator with experience of mediating conflicts elsewhere in Africa, told ANC lawmakers on Thursday that he would need only "a day or two" to complete the transition, party veteran Snuki Zikalala told the eNCA broadcaster.
In 2007, the party pushed out then-president Thabo Mbeki over allegations of abuse of power.