Property developer Stuart Robinson, who is part of the Pompey Supporters' Trust, has agreed a deal for the land surrounding the Fratton Park stadium.
Administrators David Rubin & Partners confirmed they have entered into an "exclusivity agreement" with Robinson.
"I hope that this will ultimately lead to the exchange and completion of the sale in due course," administrator Paul Appleton told BBC Sport.
Robinson is one of several major investors involved with the PST.
That sale is conditional on PKF first gaining permission to sell Fratton Park - controlled by former owner Balram Chainrai.
Potential new chairman Iain McInnes later added they hoped to do a joint deal for both the land and stadium as they continue their quest to take full control of the club.
That land had been owned by Miland Development 2004 Ltd but was put up for sale after it went into administration.
The land is almost 10 acres of car park and office space to the north and west of the stadium and is seen as pivotal to the club's future as it would finally allow Fratton Park to be developed.
It was initially bought by former owner Milan Mandaric in 2004 and 2005, and then passed to the club's next proprietor, Sacha Gaydamak.
The London-based French-Israeli businessman held on to the land as security for money he claims he was owed by the club until he also placed Miland into administration last year.
But the land is deemed to be practically worthless without control of Fratton Park, as Portsmouth City Council will not grant planning permission for anything on the site unless Pompey's existing stadium is upgraded or they get a new arena elsewhere.
And if the Miland acres can be reunited with Fratton Park, it would enable a new owner of the club to forge ahead with a complete redevelopment of the site.
Fratton Park is controlled by Chainrai who is owed around £17m by the club and holds a fixed charge over the stadium as security.
Chainrai recently suspended his bid to take control of the club - who are £61m in debt and have been in administration since February.
The PST have offered him £2.75m for the ground but he has refused to sell so administrator Birch will now go to the High Court of Justice and ask for Chainrai's fixed charge to be released - forcing him to sell at the market rate.
Chainrai and a group of Scottish investors led by businessman Harry Kerr called Portco Ltd had also hoped to buy the land.