Reports in Nigeria claimed that Keshi, who has been in the job since 2011 and won the Africa Cup of Nations last year, had agreed terms to take over South Africa after the FIFA World Cup.
The SAFA rejected that claim in a statement released on Tuesday but did add that an appointment would be made following the tournament in Brazil.
"That article... is devoid of any truth as SAFA will only make the decision on the appointment of the new coach mid-July," said SAFA president Dr Danny Jordaan in the statement.
"Keshi's name is among the various names that have been thrown around by the media. SAFA has not yet arrived at any decision regarding the appointment of the new senior men's national coach. That decision will be pronounced once the World Cup is over."
Keshi still has a year left to run on his Nigeria Football Federation contract but his stock will rise further if he can guide his charges to the second round.
Nigeria only need a point against Argentina in their final Group F fixture on June 25 to guarantee qualification, but could progress even with a defeat.
The SAFA announced earlier this month that coach Gordon Igesund would not be offered a new deal, with his current contract set to expire in August.
