The Scottish Football Association is on the hunt for a new national team boss after McLeish was axed on Thursday.
Killie boss Clarke is among the favourites to be his replacement and ahead his side’s clash with Aberdeen on Saturday, he was asked if he had the desire at any stage to manage the national team.
He said: “Yes, at some stage. Whether it is now or not is a matter for you guys to talk about and speculate.
“I am fully focused on finishing the season well here at Kilmarnock.
“I don’t speculate, there is no point in doing that. I know how football works. I am fully focused on this job here.”
Celtic boss Neil Lennon believes the next Scotland manager should be Scottish as he ruled himself out the running.
Asked if international management was something that would interest him, the Northern Irishman said: “No. I like the day-to-day stuff.
“The Scotland job should be – whether you think this is antiquated or not – (for) a Scotland man and there is plenty of good candidates in line for the job.