Ruth Black, a key ally of the city council's disgraced former leader Steven Purcell, was spoken to by officers in London Road police station yesterday.
Police are understood to be investigating whether Mr Purcell, who stood down earlier this year after it emerged he used cocaine, used undue influence to secure funding for a contract for Ms Black.
An official spokeswoman for Strathclyde Police refused to comment on the nature of the investigation with which Ms Black was helping detectives.
Allegations, however, are thought to centre on 50,000 of council support which a group led by Ms Black received to set up a gay and lesbian drop-in centre in the city.
SNP councillors had complained when Ms Black's new group, called Castro, won funding ahead of a more established organisation, Glasgay. Ms Black was yesterday unavailable for comment. She has previously said that she is not paid by Castro.
The new centre was needed to replace a similar body, once led by Ms Black, which collapsed with debts of 300,000 last year.
Ms Black represents Glasgow's Craigton ward.