PKF, the south coast outfit's administrators, announced on Thursday afternoon they had received a rival offer from former Football League chairman Keith Harris.
However, the Football League have subsequently released a statement reiterating their stance that no new offers will be considered so as to avoid "uncertainty".
It read: "The League had previously been informed by PKF that its preferred bid for the club was from the Pompey Supporters Trust (PST) and all parties have been focused on a successful transfer of share to that consortium.
"Given that the Football League's Insolvency Policy prohibits a club from beginning two consecutive seasons in administration, the board took the view that any change of preferred bidder at such a late stage would only create further uncertainty and was not in the wider interests of the League and its member clubs.
"Therefore, the League has informed the administrator that it will not currently consider transferring the club's share in The Football League to a new bidder.
"This means that in the event that the PST bid does not succeed and Portsmouth do not exit administration before the end of the current playing season, the club will lose its membership of The Football League."
The latest developments come just a week before a high court hearing - which has already been adjourned on three occasions - to decide the club's fate.