White, who masterminded South Africa's second World Cup triumph earlier this month, yesterday voiced his interest in coaching England.
The beaten finalists, who surrendered the Webb Ellis Trophy to the Springboks with a 15-6 defeat, are in the process of conducting a review of the tournament.
Head coach Brian Ashton has yet to receive the full backing of Twickenham chiefs, who will wait until the review is completed next month before deciding whether to extend his contract.
White described the England job as a "great opportunity for any coach" and he could be available for any possible vacancy following the apparent end to his three-year Springbok reign.
An SARU statement read: "The panel to appoint the national coach met today in Johannesburg to further discuss the process and to finalise the shortlist for the position of Springbok coach.
"SARU has confirmed that Jake White did not apply for the position and he was therefore not considered.
"SA Rugby recently met with White to discuss the matter and can confirm that White advised SA Rugby that he does not want to make a decision on his coaching future at this point in time.
"The panel has therefore compiled a shortlist of four candidates and their names will not be released until they have been informed."
White's contract officially ends on New Year's Eve and he is expected to take South Africa to Europe for Tests against Wales on November 24 and the Barbarians a week later.
The 53-year-old reportedly has a clause in his contract allowing him to be reconsidered for the Springbok position without reapplying.
Whether he wants to continue in what is probably world rugby's toughest job remains to be seen, especially as his success at the World Cup effectively allows him to name his price.
Any availability will certainly register on the radar of England's director of elite rugby Rob Andrew, who is overseeing the Rugby Football Union's review.
White's credentials are impeccable but if Ashton does depart next month, recommending an overseas candidate as his successor might prove problematic for Andrew.
Harlequins director of rugby and former England number eight Dean Richards is one of the leading contenders to profit should Ashton's contract, which expires in December, not be extended.