Last week's High Court hearing, between club administrators PKF and former owner Balram Chainrai's company Portpin, was postponed to allow further discussions to take place.
A judge adjourned the case until January 15 but gave all sides the option of making an earlier court application on 48 hours' notice.
The PST's bid hinges on the outcome of the case, at which PKF want to secure the sale of the club's Fratton Park stadium from Portpin to the fans' group.
PST chairman Ashley Brown said in a statement: "Whilst it was very frustrating to be subject to a last-minute problem which was outside our control, we have used the last 48 hours to ensure our plans are flexible enough to accommodate different outcomes if we need to, in what the judge has described as a 'fluid' situation.
"We will update you further as soon as circumstances permit, but, for now, we can assure you of three things.
"We have the funding to succeed, providing we continue to convert pledges. Our individual 'high-net worth' investors have lodged a seven-figure sum in escrow, and pledges are coming in ahead of target.
"And, of course, your money less the small administration fee will be returned if our bid is unsuccessful. Our bid has the confidence of the administrators and the Football League. That has not changed.
"We fully expect to be the next owners of Portsmouth FC, and believe we will proceed with the purchase of the club in the next few weeks."
Portsmouth were placed in administration in February and there are fears the club will be liquidated if the PST do not complete their takeover.