According to sources, Zweli Mkhize is experiencing a late surge at the African National Congress convention in Johannesburg.
About 4,426 delegates are up for grabs in the race between the candidates.
The victor will represent the party in the 2024 general elections.
Ramaphosa would continue to serve as president if Mr. Mkhize wins, but he would take over as ANC leader.
Prior to the conference, Mr. Ramaphosa had been under fire for an alleged cover-up involving the theft of a sizeable amount of foreign currency that was stashed in a sofa at his private farm.
Although Mr. Ramaphosa has denied any wrongdoing, an independent report commissioned by the speaker of parliament suggested that he may have broken the law.
On Tuesday, ANC lawmakers were told to support Mr. Ramaphosa and reject a move to launch an impeachment procedure. Only a select few defied the whip, getting beyond a significant obstacle that would have eliminated him from consideration for party leadership.
On Friday, some attendees heckled Mr. Ramaphosa, with others holding signs bearing the name of the farm on which the robbery occurred—his Phala Phala farm.
The words “change” and “He [Ramaphosa] is not coming back” were also shouted by Mr. Mkhize’s followers.
After suspicions that a communications company connected to his family benefited from a contract at the height of the Covid epidemic surfaced, the former health minister was forced to resign from his position last year. He has said he did nothing wrong.
Prior to the vote, which is anticipated to be concluded later on Sunday, advocates for the six top positions and the party’s presidency have been actively lobbying.
