Caldwell has been out of work since he was sacked by the Spireites in September.
He had been unable to keep Town in League One after taking over from Danny Wilson in January 2017 and a poor start to this season in League Two cost him his job. In 29 matches as Spireites manager he won three times.
Previously, he had guided Wigan to the League One title, having made 55 appearances for his country as a player.
On his application to be Scotland boss, Caldwell told BBC Scotland: "If I didn't believe I could make an impact then I wouldn't put myself forward.
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"I don't think that having vast experience is going to give you that much of a difference.
"International football in the past used to be that somebody had a career [in management] and it was one of their later jobs.
"Nowadays, it's a job for younger people. A new, fresher approach is going to give you more benefit.
"I only want the job because I feel I can make a difference. A club job is different. You want a job because you want to work.
"The international job, I feel that I can make a difference. Not just as the manager.
"I want to contribute in whatever way I can to get to get this country to a major finals."
Despite his struggles at Chesterfield, Caldwell believes it was overall a positive experience.
"In club football, there is a real short-term approach where nobody is getting the time.
"Better managers than me have been sacked when they probably shouldn't have been. It's a positive that I have that experience behind me at 35 years old.
"I also believe that I'm more qualified to be Scotland manager than I am to manage those teams. I have more experience dealing with international players.
"We have to go into the fine details because the margins at that level are becoming smaller and smaller.
"If we get everything right in terms of the preparation then I believe that we've got a group of players that can qualify."