EFF leader Julius Malema is of the view that President Cyril Ramaphosa would be making a mistake if he does not name David Mabuza as his deputy.
Mabuza postponed his swearing-in in Parliament at the 11th hour on Wednesday following allegations that he had brought the party into disrepute.
The decision followed an ANC integrity commission report, tabled at the party's special national executive committee (NEC) meeting on Monday.
Malema made reference to former ANC presidents who from the time of Nelson Mandela, Thabo Mbeki and Jacob Zuma who underestimated their deputies.
"If you make that mistake of not appointing DD, you won't make it past the National General Council. As a president you must always put your deputy next to you. If he wants peace, we all know how it started before Polokwane. Zuma said I want to clear [my name] but behind the scenes he said to us, they forced me out and we came charging."
Speculation has swirled that Naledi Pandor and Nkosazana Dlamini-Zuma could be in the running for deputy president.
However, Pandor brushed off this notion, saying the president was the one who would appoint his deputy.