The governing body plan to choose between the national stadium and a move to Murrayfield this week, however a charitable donation will ensure that Scotland stay at their traditional home.
The SFA have been reluctant to pay more than £2m, however, businessman and philanthropist Lord Willie Haughey has stepped in to offer a one-off donation to bridge the financial gap so long as Hampden remains the home of Scottish football.
Queen's Park's original asking price was £6m, however they face financial ruin if the move to Murrayfield goes ahead.
Queen's Park's ten-man committee plan to use the sale proceeds to redevelop Lesser Hampden as their new permanent home - a much smaller ground opposite to Hampden Park.
Queen's Park want written assurances that they can continue to play home games at the 52,000-seater arena if building work is not completed by the time the SFA take the keys.