The club sold the training facility at Thorp Arch, near Wetherby, in 2004 and an option to buy it back expires on October 10.
A report to the city council says that the club has been unable to borrow money from elsewhere to complete the purchase on its own.
The report says: "Due to its poor credit rating following the 2007 administration, and the effects of the recession, the club states that it has been unable to secure such borrowing. With time now running out if the option is to be exercised before 10 October 2009, the club has approached the council to see if finance could be made available using the council's prudential borrowing powers."
After October 10 the club will have no rights to buy back the training ground. The report says the training facility is an important asset for the city and that the facilities could be used in the 2012 Olympics and the 2015 Rugby Union World Cup