The Mirror said Leeds chairman John McKenzie called al-Khalifa on Thursday to make the offer.
The Sheikh would also take over the debts if he takes over on December 18th.
Leeds made no mention of the billionaire sheikh in a statement to the stock exchange on Wednesday which the market interpreted as a sign he was unwilling to back the refinancing deal.
The club's financial crisis is the legacy of wildly profligate spending on players and their salaries under former manager David O'Leary and chairman Peter Ridsdale.
The club is now facing the prospect of relegation to the First Division, an outcome which, refinancing package or not, would almost certainly force the club into administration and could even see it wound up entirely.