The ANC's national executive and working committees have instructed the top six - led by Cyril Ramaphosa - to manage the transition of power from Zuma to Ramaphosa‚ and most recently‚ to tell Zuma to step down.
Speaker of the National Assembly Baleka Mbete would not allow the motion of no confidence to happen so early, but put it on the calendar for 22 February.
Mr Zuma, who has not said whether he will step down voluntarily before his second term as president ends, has been deserted by several prominent allies in the ANC since Mr Ramaphosa took over leadership of what is the only party to govern South Africa since the end of apartheid.
The paper reported that Zuma will likely agree to do so, but not until after the State of the Nation Address later this week.
The rand, which tends to strengthen on signs Zuma could leave office, pared losses on the announcement from parliament.
Zuma has survived several no-confidence votes during his rule thanks to loyal voting by ANC lawmakers, who form a strong parliamentary majority.
Ramaphosa is in pole position to win an election next year and many in the party want Zuma out so that Ramaphosa can embark on his anti-corruption agenda. However, Zuma still has support within the top 6 with Secretary General Ace Magashule and his deputy Jessie Duarte defending his continued stay at Union Buildings.
"President Jacob Zuma, who is set to deliver the SONA, unfortunately embodies none of this", the letter said.
A group of African National Congress members convened under the banner "defend Luthuli House" says President Zuma's removal is a matter of urgency. They also tried to have have a motion of no confidence in Zuma debated before the address.
ANC spokeswoman Khusela Diko would not confirm or deny the crucial meeting on Sunday.