Tottenham set to sign Khumalo
"We're in the process of doing a deal for him," Redknapp told reporters at the club training ground.
"He's not expensive. We had him over on trial and we like him. He's got potential and we've got a tie up with Supersport so we've taken him on."
Local media reports said Spurs would pay 1.5 million pounds for the defender who was born in Swaziland.
Khumalo played in all South Africa's matches at this year's World Cup finals and scored the first goal against France in a 2-1 win, although it was not enough to prevent them becoming the first hosts to fail to survive the tournament's group stage.
"It will be a great chance for the kid," Redknapp added of the 23-year-old Supersport captain. "He's a great lad, comes from a poor background in South Africa and is desperate for a chance and we'll give him a chance."