Cyril Ramaphosa, the president-in-waiting, and the ruling ANC party have said negotiations should be concluded within days, but have given no details about how Zuma will be eased out of power.
The stalemate left South Africa's political scene in limbo, with public events canceled this week including the flagship State of the Nation address to parliament in Cape Town on Thursday.
Zuma cleared his diary of weekend engagements, but deputy president Ramaphosa is due to speak at a rally in the city on Sunday to start a year of celebrations marking 100 years since Nelson Mandela's birth.
February 11 also marks the day that Mandela was released from jail in 1990 - a key date in modern South Africa's rebirth as apartheid white-minority rule crumbled.
Zuma and Ramaphosa will "conclude" discussions on Zuma's exit within 48 hours and the outcome will then be announced to the nation, the News24 website said Saturday without naming its sources.
But Susan Booysen, a politics professor from Wits University in Johannesburg, said Zuma may fight on for several more days.