A fans' organisation says the "very existence" of Charlton Athletic is "under threat", with the takeover of the club still to be ratified.
The English Football League has started an investigation into potential misconduct in relation to East Street Investment's purchase in January.
ESI bought the Championship club from previous owner Roland Duchatelet.
But ESI is yet to provide the EFL with proof of how the Addicks can be funded until June 2021.
"The League has the right to investigate any club, official or player for any suspected or alleged breaches of its regulations, under EFL Regulation 83," an EFL statement said.
Majority shareholder Tahnoon Nimer has previously said he would invest money into the south-east London side this month.
The Charlton Athletic Supporters' Trust (CAST) says it "looks like desperate times" at The Valley, with "the prospect of the club running out of money anytime soon".
"Whilst we absolutely recognise there are bigger issues in the world outside, in football terms we are fighting for our club," a statement from CAST said.
"The EFL investigation into the takeover of the club by ESI poses both long- and short-term risks to the operation of the club, the most obvious of which are potential EFL sanctions and a lack of funds being injected into the club, leading to relegation at best, and liquidation at worst."
CAST say they have attempted to make contact with the current owners, local MP Matthew Pennycook, Greenwich Council and a representative of Duchatalet for updates and further clarity on the situation.
The EFL says it will be in contact with CAST, while Nimer says he has been in dialogue with the EFL about Charlton's financial position.
"I can confirm I have received correspondence from the EFL and I have already provided an initial response, and I intend to co-operate fully with them in order to ensure clarity on this matter," Nimer said in a statement on Monday.
Charlton are in the Championship relegation zone with nine games of the campaign remaining, but the 2019-20 season has been suspended indefinitely because of the coronavirus pandemic.
How did we get to this point?
ESI completed its takeover of Charlton on 2 January, ending Duchatelet's six-year spell as owner - during which time supporters regularly protested against the Belgian over how he ran the club.
A company owned by Duchatelet still owns The Valley and the club's training ground - with ESI expected to complete the purchase of both assets this summer.
Shortly after the takeover by ESI, Syrian businessman Nimer subsequently fell out with newly-appointed executive chairman Matt Southall and director Jonathan Heller, removing both men from the board of directors on 20 March.
Bucharest-based pair Marian Mihail and Claudiu Florica were appointed in place of Southall and Heller, and Nimer reiterated his commitment to the club at the end of last month.