The investigation centres on evidence given by Edinburgh Liberal Democrat leader Donald Gorrie, who told the inquiry he believed some planning committee members had been involved in corruption over 25 years in Edinburgh.
It is the first time a criminal investigation has resulted from evidence given to the committee.
Mr Gorrie told a hearing of the Nolan inquiry that his suspicions centred on some former councillors (LGC, 20 December 1996). He said he had voiced his concerns in the past to police officers but lack of evidence meant no action had been taken.
However, his view that corruption has been endemic within the council for some time has angered Labour leader Keith Geddes.
He said: 'There is absolutely no substance in what councillor Gorrie is saying.
'Planning committee members in Edinburgh have carried out their duties with utmost probity at all times and I do not believe for a moment that the police will bring charges against anybody.'
Conservative group leader Daphne Sleigh said: 'I would back Donald entirely and I support his concerns.
'There is no smoke without fire and I have no doubt that what he talks about has happened in the past.
'Unfortunately, while there are strict procedures in place to deal with officers who break the rules it seems to me the equivalent does not exist for councillors.'
A spokeswoman for Lothian and Borders police said: 'An investigation is under way and a file of evidence has been passed to the procurator fiscal pending possible charges. 'That is all we can say at this stage.'