Parma ended a nightmarish 2014-2015 campaign bottom of the Serie A table having been deducted points on several occasions for the club's failure to pay players and staff as they sunk into the financial doldrums.
They were declared bankrupt in March and went into administration pending the search for investors to take over the club and pay off its debts.
Despite automatically dropping into Serie B -- Italy's second division -- the club's failure to find a buyer mean they are set to drop into Serie D, the top tier of non-professional football in Italy.
American-Italian Mike Piazza and Italian Giuseppe Corrado were reported to be heading separate takeover bids in recent days.
But Corrado walked away from talks on Sunday night, and on Monday morning La Gazzetta dello Sport reported that Piazza had also ended his interest in buying the club.
"It is with great sadness and regret that I have to announce the end of talks to purchase Parma FC," said Piazza according to the Italian sports daily.
Parma had released a club statement on Saturday, which read: "Administrators Dr. Angelo Anedda and Dr. Alberto Guion announce that the deadline for submission of valid offers to buy the company is scheduled for 14.00 (1200 GMT) on Monday, June 22nd.
"In the afternoon of the same day the administrators will meet with the Committee of Creditors and the bankruptcy judge, Dr. Pietro Rogato, in order to take any appropriate decision on the future of the club."
If confirmed, it would be a spectacular fall from grace for the club that punched above its weight to challenge for Serie A honours in the 1996-1997 season.
Parma have never won the league title in Italy's top flight but during their 1992-2002 heyday claimed seven trophies including two UEFA Cups, three Italian Cups, a European Super Cup and the Cup Winners' Cup.