Pompey administrator Trevor Birch of PKF confirmed the case to determine whether he can sell the club to the PST-led bid will be heard on December 13 and 14.
"It is a relief to know we will have some certainty sooner rather than later," said chairman of the Trust, Ashley Brown. "Our understanding is the matter will be resolved at this hearing as there is unlikely to be any grounds for any appeal.
"If all goes according to plan, and our legal advisers say we have a strong case, we will take control of Portsmouth FC shortly afterwards and the process of rebuilding our club can begin.
"That is why we are urging fans to fulfil their pledges or purchase shares by that date. The more working capital we can raise quickly, the more control we will have over the situation and the quicker we can get going with our plans.
"We are very encouraged by the initial response to the share offer. There is a steady stream of pledges and new purchases of shares arriving hourly, so many that we haven't been able to count them yet.
"However, fans can't relax. This share offer needs to be a success or else there is a significant chance the club will be liquidated. There is no alternative offer on the table, so we have to make this work."