Shares in the parent company of Southampton were suspended on Wednesday after the business failed to secure additional funds ahead of a March 31 deadline.
Southampton Leisure Holdings warned that without the injection of additional finance it would be unable to continue as a viable business.
While talks with a number of parties are going on, the company said it was required to suspend its shares because the uncertainty had prevented it from posting half-year results before yesterday's three-month deadline.
The Times newspaper said the club had failed to agree an extension of its overdraft with Barclays and accountancy firm Begbies Traynor was standing by to step in as administrator.
It is possible that moves to put the club's parent company, rather than the club itself, into administration will save it from having points docked by the Championship. The team is three points from safety in 23rd position.
The report said the club will have until the end of the summer to find a buyer or face bankruptcy.
The business is heavily in debt after spending more than £30 million on a 30,000-seat stadium more than four years ago. Its debts of £27.5 million are reportedly made up of financial liabilities of £23.1 million and an overdraft with Barclays of £4.4 million.
The Financial Times said Barclays and Norwich Union, which holds short-term loan notes for the construction of St Mary's Stadium, have been in talks over renegotiating the liabilities.
Shares were suspended at 9.5p, having fallen from 34p a year ago.
It said in a statement: "The company is currently in discussions with a number of parties concerning the injection of additional finance into its business.
"Unless this funding is secured, the company will be unable to continue as a viable business for the forthcoming 12 months and is therefore unable to publish half-yearly report to December 31 2008 by March 31 2009 which it is required to do under the AIM (stock market) rules."
Former City executive Rupert Lowe returned as chairman of the company last May, having held the role between 1997 and 2006.