Igesund's deal expires at the end of August and will not be renewed following a disappointing two-year spell in charge.
Under the 57-year-old, South Africa were eliminated in the quarter-finals at the Africa Cup of Nations in 2013 before missing out on qualification for this year's FIFA World Cup.
The likes of Carlos Queiroz and Stephen Keshi have been linked with the role, although the South African Football Association (SAFA) denied reports relating to the latter taking over.
In a statement released on their website, SAFA stated their plan to name Igesund's successor a week on Saturday.
"The position of the senior men's national team needs to be ratified by the SAFA NEC," said SAFA's chief executive officer Dennis Mumble.
"Therefore, the long-awaited announcement of the new Bafana Bafana coach will be made immediately after the NEC meeting next Saturday."
