SFA chief executive Stewart Regan has declared that he wants a new man at the helm before March to help restore the pride of the national side
Levein was sacked with Scotland bottom of World Cup qualifying Group A with Gordon Strachan, Joe Jordan and Owen Coyle all strongly linked with the post.
Billy Stark is the current interim boss and the SFA are eager to get their new man in before the qualifier at Hampden Park in March.
SFA chief executive Stewart Regan has stressed the importance of getting the “best coach possible” for the job.
"The current welter of media speculation and the number of interested parties highlights the attraction of the role of rejuvenating the fortunes of the national team,” Regan told reporters.
"We will work through a list of potential candidates and arrive at a short-list, from which we will establish a preferred candidate and, finally, appoint the new Scotland national coach.
"We will carry out this process as thoroughly and as efficiently as possible.
"We are committed to appointing the best Scotland national coach possible and will take the necessary time to achieve that objective.”
Despite continuing the hunt for a new manager, Regan admitted he has been impressed by interim manager Stark, who was in charge for Scotland’s 2-1 friendly over Luxembourg in mid-week.
"As well as providing a much-needed victory, Billy has impressed us greatly by the way he has conducted himself in the role," he added.