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But Kerr's agent has confirmed that he favours a return to international football and is one of a reported 43 applicants for the South Africa job.
His agent Fintan Drury told the Irish Times: "Brian has applied. He is interested in it and it's an attractive job. He wants to be involved in professional football. Ideally, although not exclusively, he is attracted to international football."
Kerr's contract as Republic coach was not renewed after they failed to qualify for the 2006 World Cup in October.
He took over as manager of the senior team from Mick McCarthy in January 2003, when their hopes of qualifying for Euro 2004 already looked slim.
Kerr had spent six years as a highly-successful coach with the Republic's youth teams, and previously led side St Patrick's Athletic to the domestic double on two occasions.
Drury added: "They (South Africa) are looking for somebody who has international experience, but also they are keen on the technical development side, which obviously Brian has done very successfully with the FAI, so he ticks a lot of the boxes."
South Africa also failed to qualify for next summer's World Cup in Germany, prompting English coach Stuart Baxter to step down last month.
The South African Football Association (SAFA) is expected to name the new coach in February, after the African Cup of Nations.
Romanian-born Ted Dumitru is in temporary charge of the Bafana Bafana who, since being re-admitted to world football in 1992, have gone through 11 coaches in 13 years.
South Africa will not have to worry about qualifying for the 2010 World Cup as they are the host nation.