The Elland Road club are currently waiting to find out if the takeover by Eleonora Sports - an Italian group headed by Cagliari owner Massimo Cellino - from Gulf Finance House Capital will be passed.
The 57-year-old has been bankrolling the club over recent months but has recently told Leeds he will not put any more money in until a decision comes. He agreed the purchase on February 1, some 40 days ago.
Cellino faces a tax evasion case in Italy on March 18 and his bid has been the subject of intense scrutiny. He denies the allegations.
A Football League spokesman said on Thursday: "At its meeting today, the Board of The Football League gave detailed consideration to the proposed takeover of Leeds United by Eleonora Sport Limited.
"The Board discussed the eligibility of the proposed purchasers under the Owners' and Directors' Test and examined evidence of both the source and sufficiency of funding. The majority of outstanding issues have now been resolved to The League's satisfaction and the Board anticipates receiving further information on the remaining issues, from the representatives of Eleonora, in the next week.
"The Board recognises the pressing need to resolve the matter and to provide certainty to all parties. It therefore anticipates being able to reach a conclusion in the next 10 days."
The statement comes after Leeds' managing director David Haigh insisted there was "no chance" of the club going into administration without Cellino's money.
He told the Yorkshire Post: "The club is in good hands. It has money and there is no chance of the club going into administration. None whatsoever.
"I keep hearing these whispers, where people have put two and two together to make 550. We had a winding-up order recently, which caused fans to panic.
"But the club is not in any kind of precarious financial position. Either now or in the future. It is not true and never has been.
"As a director of a company, there is a test of solvency that you have to go through. Can the company meet its debts, as and when they fall? And yes, Leeds United can."
Cellino earlier this week revealed his frustration at the situation, telling The Sun: "It has been a black hole and things cannot carry on like this.
"I have to wait for the decision of the Football League before I put any more money in.
"I want to help Leeds and get to work, but I cannot do any more until I am the owner."
The off-field distractions have been married with on-field carnage, though. United were beaten 5-1 by Bolton and 4-2 by Reading on Tuesday, putting pressure on boss Brian McDermott.
He was sacked by Cellino on January 31 but reinstated a day later when the Italian realised he had no authority to do so.