Pompey, who will start next season in npower League One with a 10-point deduction after being placed in administration for the second time in two years, left all their senior players at home when they travelled to their training camp in Spain this week in the hope they would be sold.
And administrator Trevor Birch fears former owner Balram Chainrai and his company Portpin could pull out of their proposed deal to buy the club if more players are not moved on.
"Under the terms of the CVA that was agreed with creditors at the end of June, Portpin agreed to complete its purchase of the club on the condition that the wage bill was reduced through player sales and compromise agreements," Birch said in a statement on the club's official website.
"We have made progress in this respect over the past few weeks, but there is still more that needs to be done if the club is to meet the pre-conditions for Portpin's purchase.
"Time is running out and, unless I can see a greater probability of player sales and compromises being completed in the near-term, the purchase will not go ahead and the club will have to close."
Birch has also began discussions with members of staff at Fratton Park about possible redundancies.
He added: "We have spoken to all of the club's staff and players and started a redundancy consultation period.
"I sincerely hope that we can complete the sale of the club and avoid the need for redundancies - and I will continue to do all I can to safeguard the future of the club - but I believe that staff need to be aware of the situation so that they have as much of an opportunity as possible to explore other options."