Manchester City U23 coach Enzo Maresca is set for talks with Celtic about the manager's job.
The Daily Mail says Roy Keane is one of a list of candidates the Parkhead club have already spoken to.
Red Bull Salzburg's American coach Jesse Marsch admitted he was 'honoured' to emerge as a target before opting to stay put in Germany, while Manchester City U23 coach Maresca and ex-Sheffield United boss Chris Wilder are also interested.
Scotland boss Steve Clarke has also been heavily linked with the role.