Jordaan, general secretary of the South African Football Association (Safa) and head of his country's campaign to stage the world's biggest football tournament, said he was "optimistic" of success this second time around.
South Africa lost their bid to host the 2006 tournament by one vote to Germany.
"Our experience of what happened for the 2006 bid has shown that there's no guarantee that you will be successful up until the final minute," Jordaan said.
"I am optimistic though and we'll be working hard."
Host to the world
South Africa are now confirmed by Fifa - along with Egypt, Libya, Morocco, Nigeria and Tunisia - as having formally declared an interest in hosting the tournament in seven years' time.
And Jordaan pointed out that the World Cup was one of the few major events the country was yet to hold since its return from political isolation.
"I think in terms of countries hosting major events, especially sports, South Africa has the most experience of the six and the most impressive record," Jordaan argued.
"We've already hosted the rugby World Cup in 1995, Formula One races, the athletics World Championships and the United Nations conference on racism, so from a major events point of view, we have an impressive record.
"The only missing link is hosting the showpiece for the most played and supported game in this country and arguably the world, which is of course the World Cup.
"Soccer is something that drives our nation and hosting the World Cup is a dream of ours that we hope to make a reality."