The party's "top-six" leadership team is due to meet Zuma later on Sunday, party secretary-general and top-six member Ace Magashule told local media including news channel eNCA and the City Press newspaper.
"Our view is that there should be a change of guard".
The ANC's National Chairperson Gwede Mantashe has told a congregation at a church in Katlehong that the party will discuss what is best for the country with President Jacob Zuma on Sunday evening.More news: An opening for Trump to fire Rod Rosenstein
They remained tight-lipped as the talks ended but have called a meeting of the party's national working committee for Monday. While Zuma's second and final term is only due to end next year, his immersion in a succession of scandals has eroded support for the ANC and many with the party's ranks want him to go before he delivers the annual state-of-the-nation address on February 8. "Go to him and say "look we're not booting you out but we think we can work better this way", he said.
But will it be given by President Jacob Zuma, still formally the head of state, or Cyril Ramaphosa, the newly elected leader of the ANC?
Mr Malema was one of the first to disclose that Mr Ramaphosa had won the race to succeed Mr Zuma as ANC leader in December.More news: Akshay Kumar aims to bust period taboo with #PadManChallenge campaign
The rand, which tends to strengthen on signs Zuma could leave office, pared losses on the announcement from parliament.
In its letter requesting the vote, the EFF said Zuma was not a suitable head of state as he is likely to be embroiled in a judicial inquiry into state corruption.
This was to avoid him facing a motion of no confidence in Parliament, brought forward by the Economic Freedom Fighters, on February 22 as well as possible impeachment, the rules of which are set to be finalised before the joint rules committee's last house sitting for the term on March 15. The embattled Zuma told supporters at his 75th birthday bash in Soweto, Johannesburg a year ago that he would resign should the ANC ask him to do so.More news: Missing woman found on latest season of 'The Bachelor'