The Portsmouth Supporters Trust has received the backing of the City Council in its attempts to save the stricken club.
The Trust is now urging administrators looking for a buyer to meet them as soon as possible to discuss the crisis.
Italian businessman Joseph Cala wants to buy the club and would pay off the £1.6m tax bill immediately but says he is willing to work with supporters.
"Without fans, football isn't fun or passionate," Cala told BBC Sport.
On 3 January, Portsmouth were issued with a winding-up petition by HM Revenue and Customs and will appear at the Royal Courts of Justice on 20 February.
But the Portsmouth Supporters Trust met with local businesses on Thursday in an attempt to form a consortium to help save the Championship club.
The meeting was said to be constructive and they have the backing of the City Council.
Pompey's parent company, Convers Sport Initiatives (CSI), entered administration in November, forcing the club to search for new owners.
CSI's administrator Andrew Andronikou revealed on Friday that Pompey have missed two tax payments of £800,000 to HMRC.
And there is an urgency to complete a deal with fresh backers, as investment is needed if Portsmouth are to meet further ongoing running costs.
BBC South understands any purchaser would need to provide £12m as proof of funds and assurances they could meet another £20m in repayments to former creditors, Balram Chainrai and Alexandre Gaydamak.
Cala withdrew an offer to buy the club last Friday after failing to agree terms with the club's major creditor, Portpin, which is controlled by Chainrai.
However on Thursday, Cala said he had renewed his interest in Portsmouth and had instructed his banker's to deal directly with Portpin.
BBC Sport has since learned he has now submitted a new offer and wants to purchase the debenture held by Portpin.
Purchasing that debenture would give Cala power to take ultimate control of the club off Portpin - something previous owner Vladimir Antonov failed to do.
But following the news that Portsmouth had been issued with a winding-up petition, Portpin may now feel this is a better time for them to sell.
Cala told BBC Sport his U-turn was based on "learning the true facts of the Debenture Note", and vowed to pay off the outstanding tax bill "immediately" if he took control, in order to keep the club out of administration and avoid any punishment from the Football League.
He added: "As soon as I am the owner or the Debenture holder, I'll always work with the fans."