The winding-up petition issued to Leeds by Sport Capital has been adjourned but the case remains live and the club have been ordered to pay back £958,000.
BBC Radio Leeds understands they have until 23 June to pay back the money.
The money was given to the Championship club as a loan, but the date for repayment was missed and the company issued the winding-up petition in May.
This is the second time this year the club have been issued with a winding-up petition by an investor after former sponsor Andrew Flowers served them with one before withdrawing it when Cellino repaid the £1.5m he was owed.
The Italian also had to pay a tax bill in the region of £500,000 and the remainder of players' deferred March wages after taking over in April.
Leeds finished 15th in the Championship this season and Cellino has said the club must be "healthy" before it can challenge for promotion back to the Premier League.
They are currently looking for a new head coach after Brian McDermott left the club at the end of May.