Bafana drew 2-2 against Morocco on Sunday to finish top of Group A and advance to the playoffs. They will face Mali at Moses Mabhida Stadium, in Durban, on Saturday.
When Igesund was appointed, he was given a mandate to reach the Afcon semi-finals and ensure the team qualified for the 2014 World Cup in Brazil.
Safa spokesperson Dominic Chimhavi would not confirm on Wednesday if the coach's job was in jeopardy, with the national federation remaining circumspect on the subject, despite media reports that his job was safe, regardless of the team's Afcon progress.
"He has a mandate to make the semi-finals of Afcon or qualify for the 2014 World Cup," Chimhavi said.
"He is very much in our plans and we are very positive he will achieve both mandates."
No need to raise any alarm bells
Safa president Kirsten Nematandani had said last week that Igesund may keep his job, even if his side failed to make the penultimate round, and the national federation was pleased with his efforts after seven months in charge.
"At this point in time, the coach has a contract with us and we are just honouring that contract, and he is doing a very good job for us as a country," Nematandani said.
"There's no need to raise any alarm bells about the coach's future. Of course you could be concerned about the targets that were set, but any other contract would have a performance contract clause.
"We were just clearing up that his job is not done."
Qualifying for the World Cup and progressing further in the Afcon tournament would be judged separately, as the second part of his mandate would only be determined later in the year.
"We have two targets – one is the Afcon and qualifying for the 2014 World Cup. Unfortunately the tournaments are not taking place simultaneously."
Safa did, however, confirm that Bafana players would receive bonuses, which would be determined by their progress in the knockout phases of the continental competition.
Igesund said earlier the Bafana players had agreed not to receive bonuses until they reached the knockout stages of the competition.
While he could not confirm figures, Chimhavi said the players would be paid according to their results.
"A group of senior players got together to discuss how the bonus issue would be handled," Chimhavi said.
"They agreed failure to make the quarterfinal stages, at least, would be seen by many that they're only in it for the money, which is not the case.
"They agreed the bonuses will be structured gradually – if we make the semis and if we win the tournament, it will be more." – Sapa