But administrator Andrew Andronikou insisted weekend talks could lead to a "satisfactory conclusion".
The club have been in a precarious position since the most recent plan to exit administration was vetoed on 14 October by the Football League.
The club initially went into administration in February with debts of about £120m and received a nine-point penalty that made their relegation to the Championship almost inevitable.
606: DEBATE
The news looks bad, really bad and as a fan of this beautiful game I hope that this can be turned around
TheGreatestSportsman
Gaydamak was Portsmouth's owner between 2006 and 2009 before selling the club to Sulaiman Al Fahim.
"Despite the new owners fulfilling all the requirements of the Football League and the creditors, and agreeing and signing up to the required terms of the purchase of the club, at the 11th hour the goalposts have been moved by Gaydamak," said Pompey in a statement.
Andronikou added: "We've reached a serious impasse in our negotiations with Sacha Gaydamak and until we can reach agreement with him there is a significant risk that the club will have to be liquidated.
"We have agreed terms with every other party involved but there is now this new obstacle that must be cleared. We are trying to get Sacha Gaydamak to see sense.
"I'm hopeful that within the next 24 hours we can get the parties around the table and we can renegotiate to everyone's satisfaction."
This could be the death knell of the club
Colin Farmery - Portsmouth Supporters Trust
As well as Barclays, Gaydamak and another former owner Balram Chainrai are the club's main secured creditors.
Gaydamak has claimed he has secured debt of more than £2.2m, of which he has asked for an unspecified amount upfront.
But lawyer Guy Thomas believes the latest development is likely to be a negotiating tactic.
"This looks more like a shot across Gaydamak bow," Thomas of SA Law told BBC Sport. "Andronikou might well be hoping that the kind of public pressure that emerged with Manchester United's spat with Wayne Rooney will bring a change of heart from Gaydamak.
"Other Championship clubs will also be very concerned by the effect of this development on the league."
The last Football League clubs to go out of business were Aldershot and Maidstone in 1992.
After a poor start to the season, Portsmouth are unbeaten in their last five games and have picked up 13 out of 15 points.
They are due to play away at Hull on Saturday and the game is expected to go ahead.
"The atmosphere, I mean it's been very good lately because we're on the up on the field," said Colin Farmery, from the Portsmouth Supporters Trust.
"It's been off the field that we've had all the problems and this is perhaps going to be the death knell of the club."
The club have been in a precarious position since the most recent plan to exit administration was vetoed on 14 October by the Football League.
The club initially went into administration in February with debts of about £120m and received a nine-point penalty that made their relegation to the Championship almost inevitable.
The news looks bad, really bad and as a fan of this beautiful game I hope that this can be turned around
TheGreatestSportsman
Gaydamak was Portsmouth's owner between 2006 and 2009 before selling the club to Sulaiman Al Fahim.
"Despite the new owners fulfilling all the requirements of the Football League and the creditors, and agreeing and signing up to the required terms of the purchase of the club, at the 11th hour the goalposts have been moved by Gaydamak," said Pompey in a statement.
Andronikou added: "We've reached a serious impasse in our negotiations with Sacha Gaydamak and until we can reach agreement with him there is a significant risk that the club will have to be liquidated.
"We have agreed terms with every other party involved but there is now this new obstacle that must be cleared. We are trying to get Sacha Gaydamak to see sense.
"I'm hopeful that within the next 24 hours we can get the parties around the table and we can renegotiate to everyone's satisfaction."
This could be the death knell of the club
Colin Farmery - Portsmouth Supporters Trust
As well as Barclays, Gaydamak and another former owner Balram Chainrai are the club's main secured creditors.
Gaydamak has claimed he has secured debt of more than £2.2m, of which he has asked for an unspecified amount upfront.
But lawyer Guy Thomas believes the latest development is likely to be a negotiating tactic.
"This looks more like a shot across Gaydamak bow," Thomas of SA Law told BBC Sport. "Andronikou might well be hoping that the kind of public pressure that emerged with Manchester United's spat with Wayne Rooney will bring a change of heart from Gaydamak.
"Other Championship clubs will also be very concerned by the effect of this development on the league."
The last Football League clubs to go out of business were Aldershot and Maidstone in 1992.
After a poor start to the season, Portsmouth are unbeaten in their last five games and have picked up 13 out of 15 points.
They are due to play away at Hull on Saturday and the game is expected to go ahead.
"The atmosphere, I mean it's been very good lately because we're on the up on the field," said Colin Farmery, from the Portsmouth Supporters Trust.
"It's been off the field that we've had all the problems and this is perhaps going to be the death knell of the club."
