Lord Willie Haughey, one of Scotland's wealthiest businessmen, has offered to put up the cash to maintain Hampden as the national stadium.
The SFA have made ownership of Scottish football's historic home a non-negotiable condition of staying put and resisting a move to Murrayfield.
However, negotiations between current owners Queen's Park and the governing body have hit a roadblock over the price.
Queen's Park have lowered their original demand from £6million to £5m, while the SFA have upped their opening offer from £2m to £2.8m.
With a gap of £2.2m between the respective valuations, Sportsmail understands Lord Haughey, chairman of City Refrigeration Holdings and a former director of Celtic, has indicated a willingness to consider bridging the financial difference.
Philanthropist Haughey also sponsored the Scottish Cup between 2009 and 2011.
The SFA's seven-strong board were expected to make a final call between Hampden and Murrayfield last Wednesday but delayed their decision by seven days to allow more time to thrash out a deal with Scotland's oldest senior club.
The committee of Queen's Park were meeting last night as hopes grew of a compromise agreement, with or without external help.
Facing the repayment of £16m of lottery funding and debentures if Hampden ceases to be the national stadium, Queen's Park president Gerry Crawley is keen to secure a 'win-win' scenario which would see the SFA pay the Spiders enough money to make Lesser Hampden a venue fit to host lower-league football.
Queen's are also keen to play bigger cup games at the national stadium free of charge.
The SFA board heard detailed presentations from Hampden Park Ltd and the Scottish Rugby Union on behalf of Murrayfield last Wednesday.
A statement released afterwards claimed both parties had been asked to provide further information.
SFA chief executive Ian Maxwell said the decision 'will have a significant bearing' on Scottish football and that the additional information would 'allow a final decision to be made'.