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.
STAYING ALIVE
There was no suggestion United, who reported higher turnover of 278.6 million pounds, could collapse, but Sullivan said he had looked at the finances of 20 clubs as he considers getting back into the game and was staggered at what he had found.
He said too many clubs in the Premier League and Championship had borrowed against projected income from season ticket sales and television money.
"...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."
Portsmouth, who are bottom of the Premier League, are in deep financial trouble and have paid their players salaries late three times this season.
The club also face a winding-up order from the government and go to the High Court on Wednesday to argue the Value Added Tax portion of their tax debt is too high at 7.5 million pounds.
