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.
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"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."