Zuma, whose tenure has been engulfed by corruption scandals, is due to deliver the annual state of the nation address on Thursday, despite growing calls for him to quit.
The African National Congress (ANC)'s 26-member national working committee meet at Luthuli House, the party headquarters in Johannesburg.
Scuffles erupted outside the building as Zuma supporters clashed with rival ANC activists with at least one woman kicked and beaten with sticks, an AFP reporter witnessed.
But Zuma loyalists have said that the president should complete his second and final term in office, which would end when elections are held next year.
Also Read
ANC spokeswoman Khusela Diko said that meeting started mid-afternoon and confirmed it was due to discuss Zuma.
Today's meeting cannot directly oust the president. But it has the power to convene the national executive committee, which would be able to "recall" him, effectively forcing him to step down.
Many graft allegations against Zuma have centred on the wealthy Gupta family, who are accused of unfairly obtaining lucrative government contracts and even being able to choose ministerial appointments.
Mcebisi Ndletyana, politics professor at the University of Johannesburg, described Zuma as a "major liability" for the ANC.
"I doubt that he will go quietly because his presidency has been troublesome - he has essentially used it to protect himself and evade accountability," Ndletyana told AFP.
Julius Malema, a former ally who left the ANC to form the opposition Economic Freedom Fighters (EFF) party, said the president had refused to resign at late-night talks on Sunday.
"He told them to take a decision to remove him if they so wish to do so because he didn't do anything wrong to the country," Malema wrote on Twitter, without naming his sources.
The EFF, which has often disrupted parliament, has demanded that Zuma does not deliver the state of the nation address in Cape Town on Thursday.
Zuma's hold on the ANC was shaken when his chosen successor - his former wife Nkosazana Dlamini-Zuma - lost out to Ramaphosa in a closely-fought race to be party leader in December.
On January 26, Ramaphosa said that Zuma was "naturally feeling anxious" about the transition of power.
The process would be handled "very carefully," Ramaphosa vowed.
Ramaphosa is looking to revive the economy and tackle record unemployment before the 2019 elections that come amid falling public support for ANC.
Zuma, in power since 2009, could leave office either by resigning, through losing a motion of no-confidence in parliament or impeachment proceedings. He could also be "recalled" by the ANC.
He has admitted that there has been serious corruption within the government and pledged to clean up state companies such as debt-laden power monopoly Eskom.
The ANC, which has ruled since 1994 when Nelson Mandela won the first multi-racial election, recorded its worst-ever results in 2016 local polls.
Disclaimer: No Business Standard Journalist was involved in creation of this content