Portsmouth face expulsion from the Football League unless the Pompey Supporters' Trust buys them and takes the club out of administration by the end of the season.
Earlier on Thursday, Portsmouth's administrators, PKF, received a new offer to buy the League One club from football financier Keith Harris, but the Football League said it would not accept any new bids.
"Any change of preferred bidder at such a late stage would only create further uncertainty," a statement said.
"[It is] not in the wider interests of the League and its member clubs.
"In the event 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 Football League's Insolvency Policy does not allow a club to begin two consecutive seasons in administration.
Portsmouth's administrator Trevor Birch said: "We note the Football League board's statement and will consider its implications."
PST spokesman Colin Farmery has welcomed the news that new bids will not be considered.
He said: "It's a momentous occasion because it really is now Trust or bust - the future of Portsmouth Football Club effectively appears to be in our hands.
"I think the Football League, to be honest, are actually just a bit fed up with it dragging on.
"This is a clear message to the administrators that they want this sorted out sooner rather than later and a sudden bid appearing over the horizon at the last minute is not what they wanted to hear.
"I think this now confirms the fact that it is us or liquidation and we hope now that fans will rally round to our cause."
Pompey have been in administration since February 2012 and are said to be around £60m in debt.
The PST have been approved by the Football League as well as the club's creditors.