Mkhize has long been cast in the role of underdog in the race to be president of the African National Congress (ANC) party -- a job that opens the way to being head of state.
Current President Cyril Ramaphosa's standing has been savaged by scandal - and Mkhize is making it loud and clear that, if the frontrunner stumbles further, he's waiting in the wings.
"The president says he's innocent and no one has reason to doubt that," Mkhize said in an interview with AFP, one of a string he conducted with the media ahead of the December 16 ballot.
But, he said, in a suave snipe at the scandal that has left South Africa agog, "I don't think it's a usual experience."
Ramaphosa's political future is in doubt over accusations that he covered up the theft of a huge amount of cash at his farm instead of reporting the matter to the police.
In submissions to a three-person investigative panel, the president denied any wrongdoing.
He said the cash -- more than half a million dollars, stashed beneath sofa cushions -- was payment for buffaloes bought by a Sudanese businessman.
But Ramaphosa's explanations did not convince the panel, which raised questions about the source of the cash and said he "may have committed" serious violations and misconduct.
Their report is going to be put to parliament next Tuesday, stoking speculation that MPs could move towards a vote to remove Ramaphosa from office.
But, at the height of the storm, the ANC's paramount National Executive Committee rallied around the beleaguered president, announcing that any such move would be opposed.
Mkhize was deeply critical of that meeting.
"I wasn't able to speak," he said. "The way they ran the meeting was a very unusual, weird way."
"Whilst in the middle and people were still supposed to speak, they decided to close the meeting and say, 'Now we have an agreement,' and closed. I stood up and objected."
"It creates an impression that the views of certain members must be muzzled," he said pointedly.
However, Mkhize, a 66-year-old doctor by training, is among those whose image has been tainted by corruption allegations.
He was placed on special leave after investigators opened a probe into a 150 million rand ($10.4 million) contract for a Covid awareness campaign.
Mkhize has denied the allegations and complained against the investigation, but, he admitted, "Nobody's perfect."