Mark McGhee and Billy Davies are the bookies' favourites for the job and the SFA are keen on a Scottish boss following the success of both Walter Smith and Alex McLeish.
The appointment of German Berti Vogts - the only foreigner to hold the post - proved to be disastrous but SFA chief Gordon Smith says he would be willing to appoint a manager from outside Scotland.
"I hope it's a Scotsman but we can't rule out an Englishman or an Irishman," he told the Sunday Mail.
"The main thing is that I deliver the best person possible to get us to the 2010 World Cup.
"There is no timetable for an appointment. I'm preparing a paper for the SFA executive committee on the type of person we are looking for.
"But if someone comes to the fore who differs from the criteria he would not be ruled out. I have to be flexible.
"It's an attractive job and I've been contacted by at least half a dozen people so far. They are all of a good calibre."