Kirsten has revived India's fortunes since taking over in March 2008
Departing India coach Gary Kirsten said he has been approached over the vacant South Africa job.
Former South Africa opener Kirsten, 43, who led India to World Cup success on Saturday, has asked for time to take stock and consider the offer.
"They have approached me but I've said I'm not going to make any decisions just yet," he told BBC Radio 5 live.
"I need to take some time off and clear my mind for a while after this magnificent journey."
Cricket South Africa are expected to name a replacement for interim coach Corrie van Zyl in June.
Kirsten helped India become the top-ranked Test side and the first nation to lift the World Cup on home soil.
"From a while back, we wanted to win the World Cup and become the number one ranked Test team in the world so to have achieved both is amazing," said Kirsten.
He knows our players very well and is probably the best thing to happen to Indian cricket
Mahendra Dhoni on Kirsten
"We've had incredible support but for me the credit goes to the players. They have handled huge expectation and pressure, they have worked really hard, prepared really well and when they have needed to make the big contributions under pressure they have done that."
Kirsten, who scored 7,289 runs in 101 Tests for South Africa, took the India job in March 2008, one year after the team's ignominious World Cup exit at the group stage.
In three years, he instilled the tough winning mentality that was encapsulated on Saturday when India chased down a target of 275 to beat Sri Lanka with 10 balls to spare.
"Everyone knows what he has done for the team," said India captain Mahendra Dhoni, whose unbeaten 91 from 79 balls drove the team over the finish line.
"He knows our players very well and is probably the best thing to happen to Indian cricket."
Kirsten paid tribute to Dhoni, whose previous highest score in the tournament was 34.
"Cometh the hour, cometh the man," he said. He saved his very best for the final."
India's players dedicated their victory to batting icon Sachin Tendulkar, who finally has a World Cup winner's medal at the sixth attempt, and Kirsten was full of praise for the man they call the "Little Master".
"I think he is the greatest sporting role model I have ever met in my life," he added. "I have thoroughly enjoyed working with him. We have become good friends over an incredible period of cricket."
Van Zyl, who
took over from Mickey Arthur last year,
chose not to have his contract renewed after the World Cup and has instead reclaimed his post as head of the country's high performance centre in Pretoria.
Cricket South Africa has drawn up a six-man shortlist for the job that is reported to include former England coach Duncan Fletcher and ex-New Zealand captain Stephen Fleming.
Meanwhile, India have been fined for bowling at a slow over-rate during the final. Skipper Dhoni has been docked 20% of his match fee, while his players received 10% fines.
Highlights - India record historic World Cup win (UK users only)
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