Mr Dornan insisted he had acted in "good faith"
The man chosen by the SNP to fight the by-election in the seat of former Commons Speaker Michael Martin, has withdrawn after newspaper allegations.
James Dornan said in a statement he was taking legal advice on whether he had broken charity law.
The SNP opposition leader on Glasgow City Council insisted he had acted in good faith, but did not want the issue to overshadow the election.
His party will hold another selection meeting for the Glasgow seat.
The Sunday Herald newspaper said public records showed Mr Dornan had signed all his assets over to an insolvency practitioner in October 2004.
He had used a "protected trust deed" to keep creditors at bay, an alternative to full blown bankruptcy.
The use of the deed meant he was not barred from elected office, but it was unclear if it should have disqualified him from his role as "partner director" with Culture and Sport Glasgow, a charitable organisation set up by the council.
In his statement Mr Dornan said: "In light of a report in one of today's newspapers, I have decided to step aside as the SNP candidate in the Glasgow North East by-election.
"In doing so, I want to make clear that I am not ashamed of having experienced financial difficulties in the past. Many people know only too well how that feels.
"I am taking legal advice on the suggestion that there may have been a technical breach of charities legislation by virtue of me being appointed a partner director of Culture and Sport Glasgow by Glasgow City Council, a position for which I received no financial gain whatsoever.
"However, I am absolutely clear that throughout the period of the Protected Trust Deed, I acted in good faith. I took advice about its implications and was advised that it was not a bar to holding public office.
"However, I am not prepared to allow this issue to overshadow the by-election or to be exploited by Labour as a distraction from the real issues of the campaign."
A spokesman for the SNP described his decision as "honourable".
"He is clearly putting the interests of the SNP and the Glasgow North East constituency ahead of his own," the spokesman said.
"There is absolutely no shame in experiencing financial difficulties.
"Many people - particularly in this economic climate - know what that is like. Nor is having a Protected Trust Deed any bar to holding public office or being a candidate for election."
Mr Dornan defeated former BBC Scotland journalist David Kerr by 17 votes to 12 in the selection meeting for the seat.
The by-election, prompted by the resignation of Michael Martin, is expected to be held in August or November.