Sullivan, who sold his stake in Birmingham to Hong Kong businessman Carson Yeung last year, said many clubs had put their future in jeopardy by borrowing against future income and that the state of football finances was "frightening."
"We've looked at 20 clubs since we left Birmingham. The state of the finance of football is frightening, and I think there's a possibility one Premier League club could go," Sullivan told the BBC.
"I think probably odds on one club will go," he added.
He was speaking the day after Red Football Ltd, Manchester United's holding company, reported a pre-tax profit of 48.2 million pounds in the year to end June 2009.
However, profit was boosted by the world record transfer of United's Portugal winger Cristiano Ronaldo to Real Madrid for 80 million pounds. United also plans to raise about 500 million pounds through a notes offering to refinance existing debt.
"...many, many clubs have pre-sold their Premier League income, television money," noted Sullivan.
"They've borrowed against one and two and three year's season-ticket money. They've borrowed against everything.
"There are several Championship sides absolutely on the line at the moment. It's a question of whether they can sell players for sufficient money to stay alive.
"But there's not a lot of money out there to buy players at the moment. Even some of the clubs who you think have got money really haven't got much money to spend on players."
