The Portsmouth Supporters Trust are pushing to have a financial stake in the stricken club.
Portsmouth were issued with a winding-up petition by HM Revenue and Customs over unpaid tax on 3 January.
The trust wants to negotiate for the chance to issue shares to fans with any new owner but will also meet with local businesses on Thursday to save Pompey.
"We have to make every effort to save the club," Scott Mclachlan from the Supporters Trust told BBC Radio Solent.
Pompey's parent company Convers Sport Initiatives entered administration in November, forcing the Championship club to search for new owners.
So far no deal has been struck and on Saturday the club revealed they had missed their last two payment to HMRC, believed to be £1.6m.
The club released a statement on Tuesday saying they may now be forced to sell players to meet ongoing costs, while the threat of administration is a very real possibility.
Pompey fans, business leaders and politicians will meet on Thursday to find out how best to save Portsmouth from going under and could unite to buy the club.
Mclachlan admitted time was running out to save Pompey and it may now be left to the fans to do that.
"There is the possibility there could be a community fans buy-out," Mclachlan added.
"But given the sums the administrator is talking about it would have to be a partnership with somebody for fans to get involved.
"It would be impossible for fans to get together such a huge amount of money is such a short space of time.
"Having said that, a community bid means it is the community and the city and local businesses, and you would have various partners and some sort of council involvement and central funding from government.
"There has to be an enormous reality check from the current owners about how much they want to get back from a club and a business that is clearly stricken.
"Balram Chainrai has certain expectations but there has to be an exit strategy because the fans are clearly fed up about all of this. Time is running out but I think things will move very quickly for whoever wants to buy the club.
"We have to make every effort to save the football club, whether that is a buy-out or working with potential new owners who eventually do a deal."
Mclachlan cited the example of Swansea City who were part saved by the fans several years ago.
"Swansea City have a 20% trust and a person on the board representing the fans," he added. "Brentford, Exeter and AFC Wimbledon are other examples. This is the way forward for football now.
"We are talking to people who are hoping to purchase the club and they are very keen to work with us. Once the club is purchased then the talks can begin about how the trust can get involved.
"The reality is the club is in deep, deep trouble and the next week is vital in its continuation."
But should the unthinkable happen and the present club get liquidated, then Mclachlan said they are prepared to take on a new club lock stock and barrel.
"If the club goes into liquidation that would involve the death of the football club ad no wants that. It would break a lot of hearts," he said.
"But yes starting again would allow the fans to take control but we would prefer someone came in and bought the club and ran it properly and involved the fans."