ANC President Cyril Ramaphosa, who attended a sermon at the St George's Cathedral on Sunday morning, is still on course to speak at 15:00 at the Grand Parade in Cape Town.
"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.
Mantashe said ANC officials would meet on Saturday to discuss the transition, but Zuma will not be part of the meeting.
Zuma's spokesman did not respond to calls seeking comment.
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?.
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".
The young Zuma said the family had no direct knowledge of how the talks between Zuma and Ramaphosa were going.
He is also reportedly seeking legal protection for his family and other associates who have been involved in controversial deals.
"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.
After missing out on becoming Nelson Mandela's deputy when the anti-apartheid icon swept to power in 1994, Ramaphosa withdrew from politics, switching focus to business.
Outside the church Ramaphosa told a throng of awaiting journalists: "They were praying for us and they were praying that we should have wisdom, have total commitment to the people of South Africa and that is what we were praying for".
"As we emerge from a period of difficulty, a period of disunity and discord, this Nelson Mandela centenary year offers us what I would call, a new beginning".
Zuma had been due to officiate at a diplomatic awards ceremony in Cape Town today, according to his office, but that event has been postponed.
Zuma has not said whether he will resign voluntarily before his second term as president ends in the middle of next year.
He is still fighting almost 800 counts of corruption over an arms deal from the late 1990s and his ties with the Gupta brothers, a family of wealthy Indian-born businessmen, are the subject of a judicial inquiry on grand-level corruption.
This would require Zuma to give evidence in parliament before the Guptas or his son Duduzane - who could implicate him.