The party's powerful 107-member national executive committee (NEC) met for 13 hours at a hotel outside Pretoria, and decided it would "recall" Zuma from his post, several local media outlets said.
"It took a brutal 13 hours, but the ANC's national executive committee has decided to recall President Jacob Zuma as head of state," the Times Live news website said, citing unnamed sources in the talks.
Other media reported that the party would write to Zuma ordering him to stand down as president, after his request for a few more months in office was rejected.
State broadcaster SABC said the ANC had given Zuma 48 hours to turn in his resignation.
ANC officials were not reachable to confirm the reports, but the party called a press conference for 12:00 pm (1000 GMT) at its headquarters in Johannesburg.
The ANC can "recall" the head of state, essentially forcing him to step down, but the process is a party-level instruction and he is under no constitutional obligation to obey.
If he refuses, he would then likely be ousted via a parliamentary vote of no-confidence within days.
As the dramatic power struggle built to a climax, African National Congress chief Cyril Ramaphosa reportedly left the all-night meeting for a face-to-face conversation with Zuma at his official Pretoria residence.