Last week, Ramaphosa cancelled a meeting of the NEC, which had been expected to push for the early removal of Zuma.
The decision comes after almost five days of talks between Zuma and the deputy president, Cyril Ramaphosa, who took over the leadership of the ANC in December.
Zuma has not said in public whether he will step down voluntarily.
A similar NEC meeting was called off last week after direct talks between Mr Zuma and Mr Ramaphosa, who is the deputy president as well as the new leader of the party.
"Should the ANC intend to do that, it will undermine the Constitution and the democracy of South Africa", says Dr Groenewald.
"We leave this church well armed with the good blessings and prayer.so as the leadership of the ANC we have been well empowered as we move ahead. and as we manage this transition", Ramaphosa told reporters.
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.
A senior ANC source told Reuters that the executive committee would meet at 2 pm (1200 GMT) in Pretoria on Monday.
Once Zuma is out, the book is likely to be thrown at him over the many charges of corruption levelled at him. "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".
Zuma's hold over the ANC was shaken in December when his chosen successor - ex-wife Nkosazana Dlamini-Zuma - narrowly lost out to Ramaphosa in a vote for new party leader. "To do so, we will draw deeply on the wisdom of Nelson Mandela", he said.
Ziyanda Peter, a 33-year-old unemployed mother of four from Langa, is looking to Ramaphosa to rebuild the ANC and revive the hope that South Africans had for a better future when Mandela led the country.
Ramaphosa said a resolution of the issue would have significant consequences for the country and for the ANC.
NEC is a key ANC decision-making body that has the power to instruct Mr Zuma to resign.
In 2008, the party pushed out then-president Thabo Mbeki over allegations of abuse of power.