The League One side have been in administration for over a year and will be expelled from the League if they are not taken over before next season.
Thursday's hearing was supposed to confirm a date for the case for administrators PKF to attempt to gain permission to sell the club's Fratton Park ground, which is controlled by former owner Balram Chainrai's company Portpin.
The court has not confirmed a date but it is hoped that could be announced within the next few days. Fans' group the Pompey Supporters Trust's bid to buy the stricken club hinges on being able to purchase the ground for around £2.65million.
A PKF statement read: "We are pressing ahead with the case that is seeking the court's consent for the disposal of Fratton Park to the PST.
"The court has this morning confirmed that the case will be heard by 19 April at the latest, which will enable us to meet the Football League's deadline for the sale of the club, subject to a favourable ruling. We hope that, in the next few days, the court will be able to set a specific date for this hearing."
The Football League have also said they will only consider the bid from the PST, having dismissed the latest rival offer from financier Keith Harris earlier this week.
But the case, which has already been adjourned four times, appears to have hit yet another sticking point over the League's stance.
The statement added: "The court was also made aware that correspondence has been exchanged between the Football League and Portpin which seems to lead to some ambiguity with the League's previous public statements that no other bid would be considered at this late stage.
"We will be seeking clarification from the League as a matter of urgency."