The ANC said that the talks meant that a special party meeting scheduled for Wednesday that could have forced Zuma out of office had been postponed to next week, but it gave no details about any possible resignation deal. "After fruitful and constructive discussions".
Mr Zuma is deeply unpopular with many South Africans after serving eight years as the nation's President.
What has felt like possibly one of the longest of political weeks in South African history is staggering towards an end, yet the postponement of another event where President Jacob Zuma would have presided seems to indicate that things could finally be drawing to a close for him.
A protracted and messy exit for Zuma won't go down well with investors, who are counting on Ramaphosa to fulfill his pledge to revive the flagging economy, create greater policy certainty and clamp down on the alleged corruption that's characterized Zuma's administration.
Zuma took power in 2009 but has been in a weakened position since Ramaphosa replaced him as ANC leader in December.
ANC party officials met with Zuma over the weekend to request his resignation, but he refused, triggering a week of dramatic political manoeuvring.
The president has been enmeshed in a series of scandals but denies wrongdoing. "We want to ensure that we are not involved in motions of no-confidence, or impeachment that will affect our party".
An anti-corruption group in South Africa is criticizing what it calls a "veil of secrecy" around talks aimed at securing the removal from power of President Jacob Zuma.
The Congress of the People's Mosiuoa Lekota says its suspicious that Ramaphosa simply can't remove Zuma when he's received authorisation from the national executive committee to do so.
Springing to the defence of her beleaguered husband, who is under enormous pressure to step down or face the prospect of a motion of no confidence vote or possible impeachment, Thobeka Madiba-Zuma wrote in isiZulu.
Parliament was supposed to debate a motion of no-confidence against Zuma on February 22.