The board has drawn up a three-man shortlist and are conducting interviews over the next few days.
Kevin Blackwell was the first to be interviewed on Wednesday. Head coach Blackwell is the favourite as he has a good understanding of the club after spending the past year at Elland Road under two managers.
Whoever does get the job may not be their for long if haulage magnate Steve Parkin takes over the club. He is currently looking into Leeds' financial records as he considers making a move.
Parkin is understood to be a fan of Crystal Palace boss Iain Dowie, but with the former Northern Ireland international striker involved in the Division One play-off final, he could soon be out of the equation.