He and senior members of the African National Congress (ANC) held talks on Sunday but no details of their meeting have been released.
Facing corruption allegations, Mr Zuma was replaced as ANC leader in December.
Party leaders, who may be trying to oust Mr Zuma before his State of the Nation address later this week, will hold an emergency meeting on Monday.
Mr Zuma, who spent time in prison for his part in the fight against apartheid, is most of the way through his second – and last – term as president.
Julius Malema, an opposition leader and former ANC member, said on Twitter that Mr Zuma had been asked to stand down but had refused.
Other unconfirmed reports from Sunday’s meeting say that Mr Zuma asked for protection from prosecution for himself and his family.
Mr Zuma’s presidency has been overshadowed by allegations of corruption.
In recent years his links to the wealthy-Indian born Gupta family, who are alleged to have influenced the government through their relationship with Mr Zuma, have caused his popularity to plummet. In South Africa, it has become known as “state capture”.
Both Mr Zuma and the Guptas deny the allegations.
Then there is also the country’s struggling economy, which has been adversely affected by political infighting in recent years.
As a result, many in the ANC fear his presidency has become toxic – and is hurting the party’s standing.
That appeared to be borne out at the 2016 local elections when the ANC lost ground to the opposition Democratic Alliance (DA) and Economic Freedom Fighters (EFF).
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