The Scotland national team head coach met with majority shareholder Dermot Desmond during the summer of 2014 after Neil Lennon opted to leave the reigning Scottish champions.
Clarke was looking for his next job after leaving West Bromich Albion in the summer of 2014. However, he was passed up for the top job at Celtic Park by Norwegian coach Ronny Deila.
He told the Scottish Sun: “At the start of that summer, I was quite confident I’d come out the other side in a job of some kind.
“I met Dermot Desmond at his place in London and we had a good chat. I was interviewed by Brighton at around the same time.
“I had two really good interviews at two really good clubs and ended up runner-up in both. Celtic appointed Ronny Deila and Sami Hyypia got the Brighton job. So it was a little lesson for me not to be too confident about getting a job in future.
“It’s nice to be wanted, it’s nice to be invited for interviews but it’s not always certain a job is going to result.”
Clarke also revealed that he was considering job offers in the United States before the opportunity arose to lead Kilmarnock. His success at Rugby Park led to him becoming Scotland boss after the departure of Alex McLeish and he’ll become the first manager to lead the nation to an international tournament when Euro 2020 begins this summer.
Though the opportunity was there to lead either the Colorado Rapids or the New England Revolution, Clarke explained why the move to Ayrshire was something of a no-brainer.
He added; “It appealed in a lot of ways. There were a lot of family reasons why it made sense. At the time we had one grandchild, but I knew more would probably be coming. I was right enough there, I’ve three now and a fourth is due in July!
“My wife and I are both close to our families, so going to the USA would have been a big call in that respect.”