Earlier during his address Mantashe lashed out at those insulting party president Cyril Ramaphosa over ongoing Zuma to force him to resign and appealed for patience.
Ruling party leaders are uncomfortable with the idea of backing an opposition motion, fueling speculation that the ANC will make an internal decision to remove Zuma in the same way that President Thabo Mbeki was ousted in 2008 during his second term.
"There is agreement on the end game, what is being discussed is the timing and the process that should be followed", Mantashe told the public broadcaster on the side lines of the party's 106 birthday celebration in Mpumalanga. "Allow Cyril Ramaphosa to execute and use his art and his personality to manage this", Mantashe said.
But Zuma's wife Tobeka Madiba-Zuma caused a stir on social media on Friday after she posted a picture on her Instagram account, @firstladytzuma, showing her and the president inside what appears to be a plane, with part of the caption reading "It's going to be ugly".
She also cautions against "picking a fight with someone who is not fighting you".
Responding to comments on her photo posting from seemingly unhappy South Africans, Madiba-Zuma reiterated her warning about rough times ahead in the defence of her scandal-hit husband.
Sources told News24 on Friday Zuma and Ramaphosa were expected to conclude talks on Zuma's exit within the next 48 hours, after which the outcome will be announced to the nation.
"Government issues and ANC issues are not family issues, therefore the family does not have anything to say regarding this".
As pressure grows inside and outside the ANC for Zuma to resign, the president and his deputy have been meeting to discuss a transition of power that Ramaphosa has indicated should not humiliate Zuma or further divide the country of 55 million people.
Professor Susan Booysen, an analyst from Wits University, added that Ramaphosa's decision to hold a meeting with Zuma indicated Zuma could no longer rely on his supporters in the top six, Ace Magashule and Jessie Duarte.