The Saints' holding company, Southampton Leisure Holdings Plc, went into administration last week, but under a loophole the club claim they should not be deducted points as it is not the club itself.
The Football League is under pressure to ensure the Saints are still deducted 10 points, which would ensure their relegation to League One. If they do not earn enough points to stay up this season, they would start next season on -10.
The League's board met on Tuesday and have comissioned an "independent forensic accountancy report in order to clarify the legal and financial position of the club, as a matter of urgency".
Southampton Leisure Holdings Plc's joint administrator Mark Fry said he has had plenty of enquiries about the company.
He told the club's official website: "The latest news is that we've had between 15 and 20 enquiries, but at this early stage it's very difficult to say how many of those are truly serious.
"Having said that, we believe that there are a number of seriously interested parties among those who have the wherewithal to acquire the club."