Kilmarnock chairman Michael Johnston will resume discussions with Allan Johnston on Wednesday over the manager's position.
Sunderland are understood to have signed forward David Moberg Karlsson from Gothenburg, subject to a medical.
The Under-21s boss was speaking after bookmakers' favourite Gordon Strachan said on Wednesday night it would be "an honour" to be asked to manage the national team, while another contender, Owen Coyle, revealed on Thursday that he would be open to an approach from the Scottish Football Association.
Stark was appointed interim boss following Levein's sacking on Monday and will take charge of team affairs for next week's friendly in Luxembourg.
After naming his squad at Hampden, Stark declined to divulge whether he would apply for the job but did not rule himself out either.
Asked if he would be interested in the role long-term, Stark said: "It's quite simple for me to answer that one. I've been the Under-21 manager and I've thoroughly enjoyed that job.
"As far as I'm concerned, I'm going to lead the team next week and we'll take it from there.
"I don't know how that process works in terms of applications.
"I've been happy in the Under-21s job and I'm honoured and absolutely delighted to have the faith of the board that I can prove myself capable of taking the team next week.
"I don't think you rule anything out in football."
On whether the position of Scotland manager would be a dream job, he admitted: "I think it's a job that every individual would covet.
"I've been very proud to be the manager of the Under-21s and I can only imagine that would be exaggerated when you're in the full job.
"My remit is to take the team through the Luxembourg fixture and that's all I'm concentrating on."
Stark - who has rested a number of regulars including goalkeeper Allan McGregor and defender Gary Caldwell - says his priority right now is galvanising a squad disappointed by Levein's departure.
He said: "I can say categorically I'm not thinking anywhere beyond this game.
"I've got enough on my plate trying to get the players lifted because they are disappointed that Craig has left. It has been very apparent that there was a real loyalty there to Craig.
"I've spoken to a few of the senior players and they are old and wise enough to know that we have to move on.
"But they are very disappointed and part of the job will be to try to lift morale and get a really positive attitude going into the game."
Stark revealed that some players feel responsible for Levein's sacking, the result of Scotland sitting bottom of their World Cup qualifying group without a win after four games.
He added: "I think there's a good group of players there who will feel that they've maybe let the manager down a wee bit.
"Good professionals - and I think this squad is full of them - will take some responsibility when they look at themselves and what they've done.
"It's my job to try to galvanise them and get them through this fixture next week. We are going to be positive and try to win the game in Luxembourg.
"From the players' point of view, they will move on from this day. They are all experienced enough to know it's unfortunately part of the football world.
"We have to have sympathy for the guy who has lost his job but we are here and we have to move on.
"They are disappointed, there is no doubt about that. But I don't have any doubts that, by the time we meet up on Sunday, we will be able to galvanise them and get a good, positive outlook."