Ramaphosa said at a party rally in Cape Town on Sunday he wanted to replace "a period of difficulty, disunity and discord" with "a new beginning" for the party.
"We know you want this matter to be finalized," he said to rapturous cheering, vowing to tackle corruption that has tarnished Zuma's government.
Zuma has clung to power after rejecting a request by his party's senior officials to resign a week ago.
The party's powerful 107-member national executive committee (NEC) were called to a hotel outside Pretoria for a meeting scheduled to start at 2:00 pm.
Cars carrying ANC leaders drew into the venue, but no official word was expected to confirm the closed-door meeting had started.
The committee could recall the president from office, though he would be under no constitutional obligation to obey the order.
"We know you want closure," Ramaphosa said on Sunday. "Because our people want this matter to be finalized, the NEC will be doing precisely that."
Political analyst Somadoda Fikeni said the committee was split, and warned some members facing corrupt allegations while serving Zuma were "not fighting for a principle or the ANC, it will be the basic instinct of self-preservation."
"They will strive for consensus, but if that fails, it will go to a vote," he told eNCA television.
"Those who are pushed into a corner will be seen as having tried to block this transition.
"The pressure is so much, it has to be the final decision for the ANC leadership. If they fail to do so, they will have surrendered the initiative."
Zuma's presidency has been marred by corruption scandals, slow economic growth and record unemployment that have fuelled public anger.