O'Neill's decision to turn down the four-year contract he would have been given as Scotland manager, opting instead to remain in charge of Northern Ireland where a new six-year deal is on the table for him, is a significant setback for Regan and the sub-committee of the SFA board charged with recruiting Strachan's replacement.
Scotland are next in action against Costa Rica on 23 March, by when they will hope to have finally found a replacement for Gordon Strachan.
The Scottish Football Association had agreed £500,000 compensation with the Irish FA to secure the services of O'Neill.
O'Neill is expected to sign a new deal with Northern Ireland.
However, O'Neill announced on Monday that he had chose to remain in his current post rather than mastermind Scotland's bid for a place at Euro 2020.More news: CNN's Sanjay Gupta Diagnoses Donald Trump With Heart Disease
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"Michael and his advisers met our delegation in Edinburgh on Thursday and discussed all aspects of the role during a three-hour meeting", he said.
However in a statement, O'Neill said it was "a great honour" to be offered the position but added it was "not the right opportunity" for him at this stage of his career.
O'Neill took Northern Ireland to the round of 16 at Euro 2016 - their first major tournament in 30 years - but they missed out on qualification for this year's World Cup in Russian Federation after a play-off defeat by Switzerland. I have always said that.
'The IFA and I have a really good relationship so I'm a little bit surprised they (the SFA) have gone about it the way they have but at this minute in time until I'm given permission to speak to anyone I'm firmly focused in the job I'm in'.