Billy Davies has withdrawn his interest in the Scotland manager's job, but BBC Sport understands he was never on the shortlist for the post.
Davies had previously expressed an interest in the job
And a Scottish FA spokesman said it was "disappointed" with comments made by the former Derby County manager.
Davies was quoted as saying that his agent had been approached by the SFA.
"We were informed they wanted to get me involved in the process. We told them we would not be taking things any further," he told the Daily Express.
"My representative got a call from the SFA to say I was on the shortlist and then he took another call to say they wanted to speak to me about the job."
The former Preston and Motherwell manager, who was recently sacked by Derby, had previously expressed an interest in the job.
But the men the SFA wants to interview are Celtic coach Tommy Burns, Motherwell manager Mark McGhee, Southampton boss George Burley and former Rangers, Liverpool and Newcastle manager Graeme Souness.
The SFA has asked Celtic, Motherwell and Southampton for permission to speak to their employees.
BBC Sport understands that Celtic are happy for Burns to be interviewed, while the SFA does not evisage any problems with the other two clubs.
Southampton have yet to respond officially to the request to speak to their manager, while Motherwell manager McGhee was believed to be speaking to his club on Tuesday.
The 50-year-old McGhee became a strong candidate after leading his side to a top-six position in his short spell with the club.
He also emerged with his reputation enhanced for his handling of team affairs after the recent death of club captain Phil O'Donnell.
But the former Wolves, Reading and Brighton boss has insisted he would only leave Motherwell with the "absolute consensus" of everyone at the club.
Burley, the only one of the four not to have led the bookmakers' odds at some point, indicated in December that he would be interested in the job.
Burns had looked to be favourite for the role in January last year, when Walter Smith resigned as Scotland boss to return to Rangers.
He had been on the Scotland staff under both Smith and Berti Vogts, and was keen to take the top job, but withdrew from the race when the SFA made no contact with him.
Former Rangers, Liverpool, Blackburn and Newcastle manager Souness is known to be keen on talking to the SFA and is presently unemployed.
McLeish quit Scotland in November to become Birmingham City manager.
The 48-year-old narrowly missed out on securing qualification for the Euro 2008 finals for his side.
Scotland's first opponents under a new manager are set to be revealed in the next 24 hours, with the SFA close to announcing the opposition for a friendly on 26 March.
However, it will not be Argentina or Nigeria - and unlikely to be Poland - as had been touted in some reports.
The SFA hopes that the new manager will be in place at a training camp in the first week of February.