Mr McCann confirmed plans to step down in spring as chairman and chief executive of the Scottish champions after five years in charge. His departure will follow Celtic's move from the junior Alternative Investment Market to the main index.
Mr McCann said he wanted to sell his 50.1 per cent stake, valued at nearly pounds 32m at yesterday's price, to shareholders and fans rather than to "faceless City institutions". He said: "I will not be selling my stake to a controlling shareholder."
Celtic's financial advisers were yesterday studying the possibility of a rights issue which would give existing shareholders first refusal on Mr McCann's stock. However, analysts believe that existing stakeholders would be unable to buy the entire stake.
Mr McCann has been locked in a battle with Brian Dempsey, a former director of the club, who has repeatedly accused him of disregarding the interests of Celtic's fans. Mr Dempsey, a wealthy property developer, was the head of a group of investors, including Simple Minds singer Jim Kerr, U2 star Bono and Scotland's biggest lottery winner, John McGuinness, which recently tried to wrest control of the club from Mr McCann.
Mr Dempsey told The Independent his group may seek to buy part of the chairman's stake if it is offered on the market after the rights issue.
Celtic yesterday announced a 38 per cent rise in net profits to pounds 7.1m despite a 14 per cent slide in operating profits due to higher players' salaries.