The announcement came on the day of a scheduled SFA board meeting to discuss the search for a new Scotland manager.
Regan insisted after O'Neill's rejection that a number of new candidates had got in touch regarding the role, which has been vacant since Gordon Strachan departed in October previous year.
"I only want the job as I feel I can make a difference". You want a job because you want to work.
"I have spoken to Stewart Regan, I've spoken to Rod Petrie and other people".
Caldwell scored twice for Scotland during his playing career, including the victor against France in a 1-0 win at Hampden. "Their love of the game mirrors Scotland's passion for football and I am proud to have served the Association".
He told the BBC: "I just feel that I have a lot to offer. The worldwide job I feel like I can make a difference and if I didn't think that I wouldn't apply for it and not just as the manager". A young person with different ideas to take the country forward.
Former Wigan Atheltic and Chesterfield boss Gary Caldwell reveals that he has applied for the vacant managerial role with Scotland.
Although the Latics were relegated, Caldwell led them to a swift return to the English second tier during his first full campaign in charge.
Caldwell has been out of work since he was sacked by the Spireites in September. During his tenure, the club was relegated and continued to decline in League Two. Caldwell departed having won just three games in 29.