Southampton's parent company entered administration in April
Prospective Southampton owners, the Pinnacle Group have asked the Football League to reconsider a ban on an appeal against the club's 10-point penalty.
Saints will start the season adrift in League One after their parent company entered administration in April.
For a takeover to be approved, the League insists Pinnacle must waive any right to appeal against the deduction.
"If they are so adamant that they were correct, why refuse us the opportunity to appeal?" said Pinnacle's Tony Lynam.
"Needless to say, we hold a different view to the Football League, and maintain the belief that we should be granted the opportunity to appeal their decision.
"This is not an issue over the 10-point deduction, more the fact that in meeting every condition within the Football League's rules, we should be allowed the right to appeal, should we wish to do so."
Lynam, managing director of the property consultancy behind the bid, previously told BBC Radio Solent that, despite the Football League's stance, they "remain totally committed to the takeover".
Pinnacle, whose group includes legendary ex-Saints player Matthew Le Tissier, saw their period of exclusivity as bidders end last Friday.
The group's representatives met the League's board on Monday, and Lynam explained: "The League explained their position regarding an agreement they wish us to enter into, concerning the position the club is in currently with the 10 points.
"The League's position is one of numerous points that we've had to overcome during the last few weeks.
"We need to work together to overcome those differences - we all want the same thing, and that is the survival of the football club.
"The bottom line is that we're still going to buy this club and we're working hard with the League and all the parties concerned."
A Football League statement read: "The Football League has the responsibility to ensure all League clubs start the season with certainty as regards the competition they compete in.
"With that in mind, the Football League has responded directly to the Pinnacle Group and will continue to liaise with their representatives."
Parent company Southampton Leisure Holdings plc (SLH) have been in administration since April, and Saints had hoped to avoid a points deduction as SLH was in administration - not the club.
But a League investigation by "independent forensic accountants" found that the football club and SLH were "inextricably linked as one economic entity" and applied their mandatory 10-point penalty, which will apply from the start of next season in League One.
Once a club has entered insolvency proceedings, the Football League must approve any takeover for the club's League share to be returned, allowing them to play in the League and its associated competitions.
Last summer, the League refused to allow Rotherham, Bournemouth and Luton to begin the season unless they accepted points deductions following spells in administration.
Lynam also indicated that the staff wage bill due later this week at St Mary's would be settled.
"I think we have to be fair to all the staff, their patience has been tested to the limit. They're clearly our top priority," he added.
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