Alex McLeish has been named as the new national team manager but Clarke was tipped as a serious contender to replace Gordon Strachan following his incredible start at Rugby Park.
Now he plans to rededicate his full attention to his current job after seeing former international team-mate McLeish land the Hampden post.
Clarke said: “The media has been pestering me non-stop about it but as far as I was concerned it was never a story.
“There was never an approach from the SFA (Scottish Football Association) and it was never encouraged from this side of the table.
“I’m happy to be here working for Kilmarnock and hopefully we can continue what we’ve been doing recently.”
Killie had just six points when Clarke was named as Lee McCulloch’s successor in mid-October.
Having fought back with 10 men to beat Dundee in midweek, they can now move into the top six with victory over Motherwell on Saturday.
However, Clarke admits he is still more concerned about the teams below his side in the Ladbrokes Premiership table than catching those above.
“After a result like Tuesday’s you get a little euphoria because it’s such a good feeling to come back from a difficult situation to win the game,” he said.
“But we have managed to calm them down over the last few days.
“There is still no reason for the lads to let things run away with themselves.
“We’ve got 32 points and that’s still not enough. We need more. We need to get further away from the bottom.
“We’re 12 points in front of bottom and nine away from second bottom. The quicker we can increase that gap the better.
“We only had six points the day I turned up. We’ve come a long way since then but we’ve still got a long way to go.
“We go to Fir Park tomorrow for a really difficult game and we’ll have to be at our very best to get something.””