Prospective Southampton owners Pinnacle Consortium have revealed they may be prepared to accept a 10-point deduction in order to finalise the takeover.
Takeover talks stalled with the Matt Le Tisser-backed group, who were told they cannot appeal against the deduction.
Le Tissier told BBC Solent: "We're confident the issues with the Football League can be resolved on Monday, even if that means accepting the penalty.
"The Pinnacle Group are still 100% committed to finalising this deal."
Saints had entered a period of exclusivity with the Pinnacle group to arrange a takeover but that passed on 19 June without an agreement.
The Saints legend continued: "Michael Fialka is a part of the group. A lot of time, effort and money has been committed and it would be silly for us not to see it through.
"There are still other clauses in the Football League document [denying the right of appeal] that we believed to be ambiguous, which we hope the Football League are able to be fair in this respect and we hope to come to an agreement on Monday.
"They're denying us the right of appeal, which we feel is not fair. But if it's the only way to move things forward, then we are prepared to maybe take the 10 points on the chin and move on.
"I've spoken to the [group] owner this morning and he's confirmed that once the Football League issues have been dealt with, it will only be a matter of hours after that that we can complete a deal."
BBC Sport
Former Southampton chairman Leon Crouch has refused to comment on speculation suggesting that Kevin Keegan may make a sensational return to the club.
Local newspaper reports have linked the relegated League One club with their former star player of the early 1980s.
Current boss Mark Wotte's contract runs out on 30 June, and he is due to clarify his position with the club's intended new owners on Friday.
But Crouch's Pinnacle group insist Keegan has not had a formal approach.
BBC Radio Solent sports editor Adam Blackmore told Radio 5 Live: "We've seen photos this morning taken on a mobile seemingly showing Kevin Keegan with Matt Le Tissier and former chairman Leon Crouch, although none with the three of them together.
"Le Tissier is due to become chairman of the new board at the club if the takeover is completed successfully, and Crouch has been helping the Pinnacle group with that deal.
"Mark Wotte is still under contract. The deal is due to be completed on Friday and then people will speak."
Former Fulham, England, Manchester City and Newcastle United manager Keegan has been out of the game since quitting St James' Park for a second time last September.
He first came to Southampton in July 1980 when Lawrie McMenemy lured him back to English football for £400,000 following three years with SV Hamburg.
Keegan spent two years at The Dell, hitting 37 goals in 68 league games.
During that time, Southampton finished sixth and seventh in successive seasons in the English top flight before Keegan left in August 1982 to join Newcastle.
BBC Sport
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