Liverpool are two months from becoming majority-owned by the taxpayer, which, the Observer reports, has become the likeliest outcome if a sale has not neared completion in that time.
The Royal Bank of Scotland's main £237m loan to the club expires on 6 October and must either be repaid or rolled over.
Liverpool's company secretary, Ian Silvester, said: "From what I understand, and that's all I can say, the urgency is there due to the pressure from the banks, so I would anticipate that something will be happening within the next four to six weeks or so."
One option open to RBS would be to put the club's parent company, Kop Football (Holdings), into administration, but that is not favoured since it would almost inevitably lead to a nine-point deduction under Premier League insolvency rules.
Instead, the Observer reports, unless one of the parties involved in negotiations to take over at Anfield follows through with a formal offer, RBS's corporate-restructuring team would assume control of Liverpool and run the club as a wholly owned subsidiary.
That would effectively put the five-times European champions in the hands of the taxpayer who, through the government-owned UK Financial Investments Ltd, holds 84.42% of the issued share capital in RBS.
"One or two in the bank are getting twitchy about getting their money back at all," a source said. "And they are incredibly nervous about the current bids. They don't regard anything as particularly serious at the moment."