The decision, which would improve Tottenham's financial prospects, could be made at a crucial meeting expected to take place on Wednesday.
A significant relaxation would cause a renewed furore, as many in the game felt that the swingeing punishment was deserved.
Sir Bert Millichip, the FA chairman, currently in the US for the World Cup, is likely to be at the meeting. He did not attend the first hearing last month.
The view now being taken by the FA is that the penalty imposed on the club - a 12- point deduction, a pounds 600,000 fine and disqualification from next season's FA Cup - was too harsh.
In particular, the points deduction is generally viewed as condemning Tottenham to a virtually unwinnable fight against relegation. The cost of dropping from the Premier League has been estimated at about pounds 7m.
Sources close to the FA suggest that the points deduction will be reduced substantially, or possibly suspended, although the fine may be increased. But a higher fine would still be less than the cost of relegation, which would mean the loss of lucrative television and sponsorship revenues.
The FA, however, is unlikely to sanction an easier sentence against Tottenham without extracting concessions from Alan Sugar, the outspoken chairman of its parent company.
Last month, in the wake of the FA's savage punishment, Mr Sugar alleged that 70 per cent - 15 - of the Premiership's 22 clubs were involved in improper payments.
Sir Bert is believed to think that Mr Sugar should formally agree to stop bringing the game into disrepute by claiming that most of Britain's top soccer clubs are in the habit of making the kind of improper payments that led to Tottenham's punishment.
The points deduction could finally be expunged once Mr Sugar had kept that promise for an agreed period.
There may also be an attempt to encourage Mr Sugar to settle his differences with Terry Venables, the England team coach and former chief executive at Tottenham. Mr Venables intends to sue Tottenham for unfair dismissal, following his ejection from the club and company last summer. The differences between the two men have resulted in allegations and counter allegations about financial practices at Spurs.
Tottenham has begun legal action against Irving Scholar, its former chairman, for his role in the illegal payments scandal which led to the toughest penalties in the FA's history.
Tottenham's current share price of 87p values the company at around only pounds 14m.
Last summer, a top firm of accountants valued the company at more than pounds 30m, but that was before the boardroom row between Mr Venables and Mr Sugar and the penalties imposed on the club last month.
Tottenham has one other option if Wednesday's appeal fails. It can go to arbitration under a system set up by the FA.
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