Labour Scottish general secretary Jack McConnell and senior Scottish officer Lesley Quinn will conduct the investigation. Disciplinary procedures will result if the allegations are proven.
Bob Gould, who was elected as Glasgow's Labour leader last April when the new unitary took over from the former district council, resigned when his comments were reported last week in the local paper but later retracted his resignation (LGC, 7 February).
Neither councillors or members would comment but one insider said: 'One thing which has not been made clear throughout any of this is whether Mr Gould is referring to votes offered in favour of his leadership bid or of others.'
Glasgow is already in turmoil as it faces budget cuts of£80.7 million and a struggle for policy control between former district councillors and their colleagues.
The Convention of Scottish Local Authorities is meanwhile considering Scottish Office minister George Kynoch's call for it to compile a central register of members' overseas trips following the row.
COSLA president Keith Geddes said: 'We will be consulting our member councils about compiling the information centrally although the information is already in the public domain and is available for inspection at council offices.'
The Accounts Commission has rejected a central register. It says adequate audit procedures are already in place.