According to reports in Holland, PSV Eindhoven coach Dick Advocaat has been lined up to replace McDermott, but the 51-year-old has insisted that it is "pretty sad" that such speculation is tarnishing the work of everyone at the Madejski Stadium.
McDermott said: "He is a decent manager but I haven't actually read anything.
"It is pretty sad to have conversations like this really I think. You have a bunch of people here absolutely trying their best to the nth degree at the club."
Reading have not won in their opening 10 games of the Premier League season.