Mr Clarke, a lifelong Forest fan, has been in talks with the club's owner, Nigel Wray, with a view to becoming chairman of the holding company, ahead of flotation later this year. He would be in charge of the business of Nottingham Forest Plc, rather than the club's football arm.
Mr Clarke has followed the fortunes of Forest since his grandfather took him there as a schoolboy and he has attended matches throughout his political career.
Larry Lloyd, a former player and now the club's press officer, said the move would not affect the position of the club's current chairman, Irving Korn. "Who better to be chairman of Nottingham Forest PLC than the former Chancellor of the Exchequer?" he said.
It is an opportunity for Mr Clarke, who is returning to the backbenches after losing his pounds 103,000-a-year Cabinet job on 1 May, to boost his backbench salary of pounds 43,000.
However, Mr Clarke told the Express on Sunday newspaper: "I have not had serious discussions about this. I have not decided what I will be doing in the future."
Self-made Mr Wray, 48, who also owns the Saracens rugby club, is out of the country and was unavailable for comment.Reuse content