Sky sources understand that the former Reading manager is on the shortlist to take charge at the Championship club.
The Elland Road outfit are on the hunt for a new boss after Neil Warnock stepped down in the wake of Monday's 2-1 defeat at home to Derby.
McDermott is now the even-money favourite with Sky Bet to become the next permanent boss at Elland Road.
Other names in the frame include highly-regarded Brighton manager Gus Poyet (9/2) and Martin O'Neill (8/1), who has only just been fired by Sunderland.
Owen Coyle (10/1) and Mark Hughes (12/1) are also managers with Premier League experience who are currently out of work.
Less likely candidates to get betting quotes include former Leeds stalwarts Lucas Radebe and Tony Yeboah, who are both 100/1.
Steve Kean, hugely unpopular with the fans during his time in charge of Blackburn, which came to an end earlier this season, is also considered a 100/1 no-hoper.