The Sky Bet Championship club could be wound up if the debt - a £950,000 loan - is not paid.
However, a barrister representing the club told a hearing before a registrar at the High Court in London that payment could be "made very quickly".
Another hearing of the case is scheduled for June 23.
The registrar was told that money Leeds owed to the taxman had already been paid - that amount was not disclosed.
"The club wants time to pay," Rory Brown, for Leeds, told Deputy Registrar Chris Garwood at the hearing in the Companies Court - which is part of the High Court.
"The payment can made be very quickly."
Lawyers said Leeds' owner Massimo Cellino had paid money owed to HM Revenue & Customs.
And Mr Garwood told the hearing: "There is nothing which prevents him paying this debt if he doesn't wish the company to be wound up."
Mr Garwood heard that the money had been loaned by a company set up by the club's former managing director David Haigh.
The company, Sport Capital, had complained that it had not been paid and had launched a winding up petition.
Leeds on Tuesday argued that the petition should be "struck out".
Lawyers said the money was loaned by Mr Haigh not by the company, and said the company was "not a creditor".
They suggested that the winding up petition had been launched to "exert pressure" on the club.
And Mr Brown said the club was in the process of investigating whether it had been "defrauded" by Mr Haigh.
He said the club was concerned that it may be "in receipt of stolen money".
Mr Garwood dismissed Leeds' application for the winding up petition to be struck out.
He concluded that Sport Capital had loaned Leeds the money and said the club was "scratching around".
He dismissed Leeds' concerns about being in receipt of "stolen money" - saying there had been no findings of criminality.