The Yorkshire club have lost four of their last five, including a humiliating 6-0 defeat at local rivals Sheffield Wednesday. They also lost in the FA Cup to fourth-tier Rochdale.
McDermott was appointed by Leeds in April last year after he was sacked by Reading who were bottom of the Premier League.
On Thursday, the Yorkshire team's Middle East-based owners said they were talking to other potential investors after a takeover led by the club's managing director collapsed.
Media reports in Britain and Italy said Massimo Cellino, owner of Serie A side Cagliari, was close to a takeover deal.
(Writing by Justin Palmer; editing by Ken Ferris)