Party leader Cyril Ramaphosa's motorcade left a marathon ANC National Executive Committee (NEC) meeting at 10:30 p.m. (2030 GMT) for Zuma's residence near the Union Buildings in Pretoria to deliver the message in person, the SABC said, citing sources.
His motorcade returned an hour later to the venue of the ANC meeting debating Zuma's fate.
The rand, which has tended to strengthen on signs Zuma could step down before his second term ends next year, extended its gains to 0.7 percent to the dollar on expectations Zuma was on his way out.
ANC officials and Zuma's spokesman could not be reached to comment.
Since Ramaphosa was elected party leader in December, Zuma has faced mounting calls from his party to end his scandal-plagued second term a year early.
The NEC meeting in a Pretoria hotel had all the ingredients for a showdown between Zuma stalwarts and those backing a swift transfer of power to Ramaphosa, the deputy state president.
Ramaphosa, 65, says he has held direct talks with Zuma over a transfer of power, and said on Sunday the meeting of the party's executive committee would be aiming on Monday to "finalise" the situation.
The party executive has the authority to order Zuma to step down as head of state, although there is domestic media speculation that he might yet refuse.
Zuma survived calls last year from within the NEC for him to quit.[L8N1IU0QO] But analysts say there is greater support for him to step down now.
The president is also facing a no-confidence motion in parliament set for Feb. 22, but has survived several similar attempts to oust him in the past.
His entire Cabinet would have to step down if the motion of no-confidence against him was successful.
Since becoming president in 2009, Zuma has been dogged by scandal. He is fighting the reinstatement of 783 counts of corruption over a 30 billion-rand (now $2.5 billion) government arms deal arranged in the late 1990s when he was deputy president.
Some within the ANC and the opposition say the Gupta family, friends of Zuma, have used their links with the president to win state contracts and influence Cabinet appointments. The Guptas and Zuma have denied any wrongdoing.
India's Bank of Baroda, which counts the Guptas as clients, has announced plans to exit South Africa, the central bank said on Monday.
Ramaphosa has put the focus on rooting out corruption and revitalising economic growth since defeating Zuma's preferred successor, Zuma's ex-wife Nkosazana Dlamini-Zuma, in the ANC leadership race.
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