The Bahrain-based Sheikh has reportedly made an informal bid to the Elland Road board.
Now three other bidders have emerged, including ex-deputy chairman Allan Leighton.
Leighton, who is chairman of Royal Mail, has excellent contacts in the City and could emerge as the most serious rival to the Sheikh and his partners.
The other interested parties are believed to be an offshore consortium and a British based group.
New owners will also have to agree a price for Leeds' shares as well as providing money for the running of the club and signing players in January.