Coach Carlos Alberto Parreira had told reporters after Bafana Bafana beat France 2-1 the night before but failed to progress from Group A that his successor had already been chosen and "it was a very good appointment".
Parreira also said an announcement would be made "very soon".
That exchange has led many to believe that Parreira would be replaced by his long-standing assistant Pitso Mosimane who has been groomed alongside the veteran Brazilian and his predecessor Joel Santana.
Parreira has even frequently punted the 45-year-old South African for the job.
Mosimane, however, told Reuters after Tuesday's game he had no formal discussion with the South African football association yet and certainly received no firm offer.
On Wednesday, the association's chief executive officer Leslie Sedibe said they still needed to go through a complicated process before making their choice.
"We will first study the reports of the World Cup, from the training camps through to the games," he told South African radio. "Then the executive committee must meet to decide and make a choice."
The choice of national coach has always been an emotive issue in South Africa with opinion divided on the merits of local expertise against foreign experience.
South Africa has employed 15 different coaches for its national side over the last 18 years, since returning from a long-standing FIFA ban from the apartheid era.
The frequency of coaching changes has earned the association a reputation for knee-jerk decision-making and, mixed in with a long list of administrative foibles, served to create an image of incompetence.
South Africa start the qualifiers for the 2012 African Nations Cup in September.
