Ramaphosa, 65, joined Zuma's Cabinet as deputy in 2014 and replaced the president as head of the African National Congress in December, providing political cover for his increasing attacks on corruption at top levels of government.
Many of Zuma's former supporters want him to resign because of his links to scandals that have sapped support for the ANC and hurt the economy.
Speculation that Zuma's departure is imminent was fueled when Parliament postponed the annual state-of-the-nation address on February 6, two days before Zuma was to deliver it. Ramaphosa, who is due to address a rally in Cape Town later on Sunday, has said talks about a transition of power should conclude in a matter of days.
Should Zuma refuse to obey the national executive's order to step down, it could tell its lawmakers to use their majority in parliament to vote him out of office, clearing the way for Ramaphosa to take over.
Then he referred to the topic that people really wanted to hear about - his confidential negotiations in recent days with Zuma over the president's exit after a scandal-marred tenure.
"Should the ANC intend to do that, it will undermine the Constitution and the democracy of South Africa", says Dr Groenewald.
Ramaphosa, who only just won a bitterly fought internal election to become president of the ANC, has the support of only just over half the members of its top decision-making body.
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Security Council resolutions as it pursues its goal of developing a nuclear-armed missile capable of reaching the United States. Kim's presence at the Olympics has presented people in South Korea and beyond with something new to know about North Korea.
Ramaphosa was addressing the commemoration of Nelson Mandela from prison in Cape Town. "This meeting is long overdue and everyone knows what we have to do, especially now that we know that the man has no genuine interest to go".
Ramaphosa told an ANC rally in Cape Town that the meeting would "finalise" the matter, but he gave no further details.
Zuma, 75, who is in power since 2009, is facing several corruption charges, which he has declined.
Sunday's rally was part of ANC celebrations marking 100 years since Mandela's birth - as well as efforts by Ramaphosa to fix the party's reputation ahead of next year's general election.
Ramaphosa said successful resolution of the issue around the presidency had significant consequences for South Africa and the ANC.
So, if he so wishes, Mr Zuma can carry on as president of South Africa even if the NEC asks him to step down.