The governing ANC party has called a meeting of its top body for Wednesday to decide on Mr Zuma's future.
Many ANC members are pushing for Cyril Ramaphosa, the new head of the party, to replace Mr Zuma, 75, as president immediately.
Although Mr Zuma retains the support of a faction within the ANC, he no longer holds a top post.
"It's really anyone's guess as to what will come out of the meeting, but Zuma's days in the office can definitely be counted in weeks, not months", said Jakkie Cilliers, an analyst with the Institute for Security Studies, a Pretoria-based think-tank. He has been weakened by the election of his deputy, Cyril Ramaphosa, as party leader. Zuma's tenure officially runs until mid-2019.
The ANC leadership meets Wednesday and could consider moves to oust him.
Sources said this was to help avoid accusations of conflict of interest being levelled against Ramaphosa because he was expected to take over from Zuma as soon as Zuma stepped down.
Magashule, who attended the meeting between the two leaders, would not confirm whether Zuma had agreed to resign, although other ANC leaders said the agreed deal would see Zuma "go in a dignified way", Times Live said. There was no immediate comment from an ANC spokeswoman.
The ANC, which was the main anti-apartheid movement for decades, has led South Africa since the end of white minority rule and drew moral standing from its association with Nelson Mandela, the country's first black president.
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The ANC supporters, who have been stationed outside Luthuli House since yesterday morning, dispersed the crowd of BLF members as they alighted from the vehicle which transported them.
Zuma who may not be around to deliver his State of the Nation Address next Thursday has denied any wrongdoing along with the influential Gupta family who are accused of colluding with the president in shady deals known nationally as state capture.
His second five-year term is set to expire next year. "I can say to you that there are different views", she said.
Chief amongst these is the immediate recall of Cde Jacob Zuma as the President of the South Africa.