The former Chelsea defender is 3/1 favourite with bookmakers William Hill. ahead of David Moyes, Derek McInnes and Scot Gemmill, who are all priced at 6/1.
The Scottish FA's Performance Director Malky Mackay is priced at 7/1, ahead of Northern Ireland boss Michael O'Neill on 12/1, ex-Scotland international duo Paul Lambert and Stuart McCall on 14s and 16s respectively, while Preston North End manager Alex Neil is a 20/1 shot.
William Hill spokesman Joe Crilly said: "Steve Clarke has done some fantastic work since moving to Kilmarnock and he is some way ahead of the chasing pack."
However, Clarke has been linked with a return to management in England, with recently-relegated Fulham understood to be interested in securing his services for next season.
Kilmarnock striker and former Scotland cap Kris Boyd reckons his manager is likely to favour another club job if he moves on from Rugby Park.
He said: "I don't know if [managing Scotland] is something he will want to do. He's been linked with a few jobs down south, bottom of the Premier League, Championship.
"He might want to stay in the day-to-day side of football. Derek McInnes, he might be looking for a fresh challenge, maybe. You've got David Moyes and people like that who are out of work.
"Malky Mackay is already in the building and it might be the only way he can get back into management."