Rhyl FC say they to need to find investment of around £175,000 if they are to avoid liquidation.
The former Welsh champions have extended a deadline to try and save the club a further nine days until 17:00 BST on 17 April.
They say they have had three offers of possible support since publicising financial difficulties last month.
However the 141-year-old Cymru North side believe only one enquiry is serious.
The club have warned they cannot meet financial obligations without an income during the coronavirus crisis.
In March the two-time Welsh Premier winners announced "significant external investment" was needed if the club was to survive the financial impact caused by the pandemic.
At that time chairman Paul Higginson set a deadline of 17:00 BST on 8 April to make a decision on the club's future.
In their latest update they say they have received two verbal and one written enquiry of potential investment support.
"Under initial due diligence by club officials two of these interests are not believed to be credible," said their statement, adding "and are awaiting clarification of the financial position of the third interested party to support their initial written expression of interest."
The statement added that, following a board meeting, the club said that anyone who could guarantee a minimum of around £175,000 worth of investment "to meet the costs to enable the club to proceed on the resumption of the playing season" should declare interest urgently.
The club say if external investment is not forthcoming by the new deadline "the unthinkable option of liquidation will become reality for all involved at the club."