The decision was made by senior party officials after lengthy talks that continued into the early hours of Tuesday morning.
Mr Zuma, who has been leader since 2009, will face a confidence vote in Parliament if he does not agree to the request.
The 75-year-old’s tenure has been dogged by allegations of corruption in recent years, and he has been under pressure to quit since December.
The ANC’s request, reported by South African media outlets, is expected to be officially issued later on Tuesday.
Cyril Rampahosa, who replaced Mr Zuma as leader of the ANC in December, is believed to have travelled to the president’s home last night to deliver the message.
Mr Zuma has always denied allegations of corruption. But in 2016 the country’s highest court ruled that he had violated the constitution by failing to repay government money spent on his private residence.
He is also facing 18 counts of corruption, fraud, racketeering and money laundering in relation to an arms deal in 1999.
Mr Zuma’s expected resignation is being dubbed “Zexit” in some sections of the South African media.