The global showpiece kicks off today with a match between the hosts and Saudi Arabia in Group A, which includes Uruguay and the Pharaohs, who are returning to the finals after a 27-year absence.
Nigeria, who have thrice reached the second round of the event, are in a daunting Group D alongside Argentina, Iceland and Croatia, with the Super Eagles opening their campaign against the latter on Saturday.
No African country has ever reached the semi-finals of the competition. Cameroon, Senegal and Ghana have gone the furthest with their quarter-final showings.
Radebe, who captained Bafana at the 1998 and 2002 World Cups, backs Egypt and Nigeria to go far this year.
"I think Egypt not because of Mo Salah, I think gradually they have been doing better," said the former Leeds United skipper.
"They have been getting better players. You see the players they have overseas, it's not just Salah. There are other players that are playing in the highest league.
"Again, I think our rivals Nigeria, I think they will go far. I think this World Cup surely two of the African teams will go further in the knockout stages and will make us proud."
Meanwhile, Radebe says he would have relished the challenge of trying to contain a talent like Egyptian hitman Mohamed Salah in his day.
"I think for me it is exciting to see him play, especially as a defender because he is the kind of player you want to be pitted against because they improve your game as well.
"I think to improve your game you've got to play against the best in the world," concluded the retired 49-year-old.