"We are disappointed at the baseless and untested allegations and request proof from anyone who has contrary evidence," national football association spokesman Dominic Chimhavi said.
"Our bid campaign was run by, among others, late president Nelson Mandela, former president Thabo Mbeki and several government ministers, who are men of integrity."
South African sports minister Fikile Mbalula said he would comment Thursday on the allegations.
US Attorney General Loretta Lynch alleged in New York that executives from world football governing body FIFA took bribes to vote for South Africa.
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Warner is among 14 officials and sports media-promotions executives facing corruption charges totalling more than $150 million in bribes.
The 2010 World Cup bidding was confined to Africa and South Africa defeated Morocco 14-10 in a vote to decide which country would be the first from the continent to stage the tournament.
South Africa had lost out to Germany for the 2006 finals.