American businessmen Tom Hicks and George Gillett are facing a demand to repay 100 million pounds of the club's 237 million pounds debt to its lenders, Royal Bank of Scotland and U.S. bank Wachovia, in July.
That has prompted them to seek a buyer for the club, which has been English champions 18 times and won the European Cup five times.
The Sunday Times had reported that Barclays would back a 300 million pounds refinancing at Liverpool that would lead to the sale of the Premier League club.
The newspaper said the bank is this weekend finalising a deal that will see it replace the club's current lenders, provide more money for manager Rafa Benitez to spend on players and install British Airways chairman Martin Broughton as chairman.
However, the source told Reuters it would be up to the new owner to make a decision over whether to refinance the club's debt. The source also declined to comment on what price the club could be sold for or when a sale is likely to take place.
Liverpool Football Club was not immediately available for comment. Barclays Capital declined to comment.
The Sunday Times said Barclays, the main sponsor of the Premier League, will replace RBS and Wachovia, and provide the Merseyside club with additional capital.
Analysts had suggested Liverpool is worth 500 million pounds but the paper said Barclays is understood to believe it would fetch far more if given time to improve its trading.
Benitez was quoted in British media on Sunday as saying Liverpool needed to bring in more players to compete and may even have to sell a few to be able to reinvest.
"It doesn't matter if it's four or five or three or five, the cost of a top class player is 15 or 20 million pounds. So with three or four players, you start counting and I think we need up to four new players," he said in The People.
"I don't think I will have to sell a big player, but it will depend on the investors so I cannot guarantee we won't have to sell. Our idea is to keep the spine of the team."
