The home of the Hoops staged this season's William Hill Scottish Cup final last month as the National Stadium was out of commission in preparation for hosting athletics and the closing ceremony at the Commonwealth Games.
As SportTimes revealed last month, the SFA have already selected Celtic Park for the crunch Euro 2016 qualifier against the Republic of Ireland in November, and an official announcement on this is due soon.
There were concerns among some within the SFA that, with the Republic having ex-Hoops boss Martin O'Neill in charge, and with player and fan connections between Celtic and Eire, it might hand an advantage to the visitors.
But Gordon Strachan is understood to be very keen the game goes ahead at Celtic Park, where, of course, he too spent a successful time as manager and which is home to Scotland players Scott Brown, Charlie Mulgrew, James Forrest and Leigh Griffiths.
As Parkhead also boasts the largest crowd capacity of any football stadium in Scotland,
and the best hospitality facilities, it has won the honour of staging this key qualifier.
The SFA plan to be back at Hampden by the start of 2015, and next season's Scottish Cup and League Cup semi-finals and finals are, once again, scheduled to be staged at Scotland's National Stadium.
However, the long-term future of Hampden is in doubt after the SFA confirmed they are looking at all options ahead of re-negotiating with owners Queen's Park.
The current deal runs until 2020. But, with the SFA's offices, medical facilities and museum all situated there, any decision to move away would involve much more than simply playing matches elsewhere.
Chief executive Stewart Regan confirmed a consultancy firm has been engaged to examine all the options for the governing body, which include securing another 20-year lease or even buying out the freehold from Queen's Park.
He said: "It is widely known that the Scottish FA's lease on Hampden Park expires in 2020, indeed this matter was discussed publicly when we launched our Uefa Euro 2020 host bid.
"I must stress that this process is at a very early stage - no proposals have been put forward or considered, and it is hugely misleading to suggest that the Scottish FA is focusing on whether to move away from Hampden Park.
"Given its historical importance worldwide and its place in Scottish football, Hampden Park remains a key pillar of the national game."