Ramaphosa, one of the richest black South Africans, has had a hard relationship with Zuma since he left his business career and returned to full-time politics five years ago, and became deputy president in 2014.
Local media said a key sticking point in the negotiations was the potentially huge legal fees Zuma is facing from prolonged court battles against multiple criminal cases.
Speaking at the Mandela celebration on Sunday, Cosatu second deputy-president: Zingiswa Losi said Zuma had to be recalled in the interest of the country.
"But if needs be, it is an ideal for which I am prepared to die", said Mandela, who died in 2013 at the age of 95.
"But if he is going to be leading on the basis of the cacophony of noises around us, he will commit mistakes - it is [for the] protection of the president of the ANC to tell analysts to back off".
He said Ramaphosa had returned Gauteng province, where the ANC's headquarters is located in the country's commercial capital Johannesburg. The two were widely expected to hold another meeting this weekend, which will signal a final decision on Zuma's future.
Ramaphosa had earlier withdrawn from the programme and was expected to continue his meeting with Zuma.
However, a presidential official told News24 that there was no meeting planned between Zuma and Ramaphosa.More news: Los Angeles Police Department Sends Three Harvey Weinstein Cases to the DA
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"We know you want closure - we will be doing so keeping our eyes on what is in the interests of all our people", he said to loud applause.
Zuma has not spoken since being asked to resign by senior ANC officials on February 4. Ramaphosa, a 65-year-old lawyer and one of the richest black South Africans, has pledged to revive the flagging economy and clamp down on the corruption that has become synonymous with the Zuma era.
"If there ever was a time when we should be working together, this water crisis is the time", he said.
After a week of "discussions" between Ramaphosa and Zuma about the imminent change of guard, South Africans have been left wondering what the way forward will be, with the big question being: when will Zuma go?. It is important that when you manage a sensitive issue never to be excited.
The ANC is under pressure to force Zuma out of the Union buildings, with party supporters and opposition planning mass protests to force him to resign.
On Tuesday, Parliament's presiding officers announced that Thursday's State of the Nation Address had been indefinitely postponed amid fears that it might descend into chaos.
With Zuma refusing a party request to resign, the African National Congress's top decision-making committee will meet on Monday.