It is widely expected that Zuma will resign this weekend or early next week, after increasing pressure from ANC leadership structures following Ramaphosa's victory at the party's elective conference in December.
Ramaphosa told an ANC rally in Cape Town that the meeting would "finalise" the matter, but he gave no further details.
But there is a growing sense of unease over the lack of information about the confidential talks between Zuma and Ramaphosa. "We know that this matter needs to be finalised, we know you want closure".
SACP Western Cape chairperson Benson Ngqentsu said: "The longer you keep president Zuma in power, the worse off for the people, the worse off for South Africa".
In his speech, the deputy president said the government will wage a "relentless war against corruption and mismanagement of the resources of our country" and that the justice system will punish the guilty.
ANC spokesperson Pule Mabe confirmed that a committee meeting was scheduled for Monday, but he did not comment on the agenda, reported eNCA.
The political opposition has criticised the private talks between Ramaphosa and Zuma, saying the president may have been pressing for immunity from prosecution in exchange for his resignation.
She posted a happy photo of herself and her husband, seemingly inside a plane, from her Instagram account, firstladytzuma, with the following caption in isiZulu: "My crush, Nxamalala, Msholozi, Maphumephethe, Inkunzi, Emidiwayidwa, Zinyane likaMnyakanya".
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Zuma expects to be subpoenaed to testify before the Zondo Commission into state capture and may very well face criminal charges relating to the arms deal corruption and Schabir Shaik soon.
He also saluted "such freedom fighters as Sheik Yusuf, Dr Abdullah Abdurahman, Cissy Gool, Alex La Guma, ZR Mahabane, Oscar Mpetha, Philip Kgosana, Ray Alexander, Dora Tamana, John Mtini, Reg September, Dullah Omar, Ben Turok, Annie Silinga, Essa Moosa, Johnny Issel, Jakes Gerwel, Archie Sibeko, Ashley Kriel and many others who were drawn from Cape Town".
"Kusazoshipha ukotshi darling. UMsholozi did not join the ANC in 1991, jumped ship nor hip hopped between the struggle and wealth accumulation". He will finish what he started because he does not take orders beyond the Atlantic Ocean.
The family also says it remains committed towards the project of nation building and expresses their confidence in the ANC leadership elected to ensure that the party remains "a vehicle to build the nation".
Ramaphosa said they would draw on Nelson Mandela's wisdom.
Speaking at a rally as part of celebrations marking 100 years since the birth of former President Nelson Mandela, he said Zuma's exit should be undertaken in an orderly fashion just as the anti-apartheid icon would have handled it.
Madiba addressed thousands of supporters at the Grand Parade that afternoon, and Sunday's event was meant to emulate that.
Zuma has not spoken since being asked to resign by senior ANC officials on February 4.