The Scottish Football Association is on the hunt for a new national team boss after McLeish was sacked on Thursday.
Killie boss Clarke is among the favourites to be his replacement and ahead of the Ladbrokes Premiership 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."