ANC president Cyril Ramaphosa has told the party's Parliamentary caucus that immunity from prosecution for President Jacob Zuma is not part of "transition" discussions.
He also assured the MPs that the talks would be concluded in a "day or two".
Ramaphosa addressed the caucus on Wednesday, flanked by party secretary-general Ace Magashule and chief whip Jackson Mthembu.
The meeting was seen as extraordinary, as the ANC usually holds its caucuses after the State of the Nation Address (SONA), which is considered the official opening of Parliament.
SONA was indefinitely postponed this week.
"Immunity from prosecution is not even on the table. It is not in my powers to give him that," the sources quoted Ramaphosa as having said.
The MPs told News24 that Ramaphosa wanted to end speculation in the media that his Tuesday meeting with Zuma involved protecting him from possible corruption charges.
National Director of Public Prosecutions Shaun Abrahams still has to decide if he will reinstate fraud and corruption charges against Zuma.
Zuma is also a subject of the inquiry into state capture, headed by Deputy Chief Justice Raymond Zondo. He has powers to recommend that those implicated should face criminal charges.
"He [Ramaphosa] was emphatic that he could not engage in anything unlawful, or engage with Zuma on anything that is not within the jurisdiction of the executive. He said he couldn't venture into that space," an MP said. The MPs said Ramaphosa said the talks would be concluded in coming days, amid growing speculation that he is due to have another meeting with Zuma on Friday.
"He said they were now finding each other on transition, which of course we interpreted as the axing of Zuma," another MP said.
ANC members are growing anxious, after Ramaphosa dramatically cancelled the national executive committee meeting after what he called a "constructive and fruitful" meeting with Zuma on Tuesday.
The NEC, which is the highest decision-making body in the party, was due to take a final decision on Zuma's future, with his detractors confident that he would have been recalled.
Since then the country has been on tenterhooks. Opposition parties and ANC members are now planning Zuma Must Go protests, piling pressure on Ramaphosa.
Some of his supporters told News24 that they were "frustrated with how he is managing the transition," demanding a speedy and more public ousting of Zuma.
"People are beginning to question his credibility and intentions here. If we don't get rid of Zuma now, we will pay for it come election time," said one supporter, who campaigned for Ramaphosa.
Another lobbyist in the Free State told News24 that those who support Ramaphosa were trying to encourage each other from feeling disheartened.
"Everyone must trust Comrade Cyril. We need to be patient and support him as he handles this matter. We know it's done. It's just a question of how," he said.
Former Free State ANC deputy chairperson Thabo Manyoni says he is fully aware of some of these sentiments and agrees with them to an extent.
"He, in terms of his public stance and as a leader of the party, must show that he is firm and at the same time fair," said Manyoni.
Manyoni said he appreciated that Ramaphosa faced a complex situation in that he does not make decisions alone, but that it was important for him to weigh his options and be seen to be acting with more vigour on the matter.
Ramaphosa has said countless times that the new leadership of the ANC would not humiliate Zuma but Manyoni said he did not believe Zuma even deserved that courtesy.
"He has humiliated South Africa more than anyone else. His removal will allow us to unhumiliate ourselves," said Manyoni.
It's either South Africa or Zuma, he added.
But a close ally of Ramaphosa has told News24 that no one understood the monster the ANC president was facing.
"That man [Zuma] does not care about this country, not even its people. I know Cyril, he will be able to handle this situation just give him a week. I know his ability when it comes to dealing with such matters," said the source.
The source, who was close to Ramaphosa, said his actions were aimed at preventing bloodshed in the country.
"He [Zuma] wanted to drag the country into civil war. It's important for this country to make sure people aren't going to lose lives. He [Zuma] doesn't care. Cyril wants to deal with this in a way that people don't lose lives," he said.