Following a meeting with SFA president Campbell Ogilive and chief executive Stewart Regan, where the national team's dismal start to their World Cup 2014 qualifying campaign was discussed, the subject of the manager's position will be top of the agenda when the SFA Board meet today.
It would cost around £700,000 to terminate Levein's contract, which has just under two more years to run.
But his employers will weigh that against what it would cost to spend any more time in the international wilderness.
Levein, who has been on holiday since last month's back-to-back defeats to Belgium and Wales, chose his words carefully when asked about his position before last night's League Cup tie between Dundee United and Hearts, where he was working as a panelist for the BBC.
But he appeared confident that he will carry on in post. He said: "I am hugely proud to be the manager, and I want to continue to do the job.
"I had a chat with Stewart and Campbell earlier in the week, and I believe I will find out one way or the other at the beginning of next week."
The two leading figures in the SFA will now relay their feelings about that meeting to the other two members of the Board, vice-president Alan McRae and second vice-president Rod Petrie.
It is business as usual for Levein, who is finalising his squad for the friendly against Luxembourg in two weeks.
"We announce the squad for Luxembourg on Tuesday," he confirmed. "So I think before that happens we will get a decision."
Asked directly if he expects to stay in the job, he replied: "I very much hope so, yes."
Meanwhile, former Celtic and Scotland star Paul Hartley, believes Levein should be given more time.
He said: "I think we have the right man in Craig. We can't chop and change managers every couple of years, we've got to give them more time to get the positive results.
"He will see it as a building job here. We know we're not in a good position, you know that as a manager.
"But players have to take some responsibility, it can't always be the manager's fault. As a team you have take responsibility for the results."