Saturday's 1-0 loss at Southampton was Reading's fourth successive defeat, leading some to suggest McDermott could be on his way out. Club chairman Madejski has been irked by such speculation about the future of the man that last season led the Berkshire club to the Championship crown.
"It is totally absurd that the manager will not be with us this time next week," he told BBC Berkshire. "In my humble opinion it's not going to happen. We have to remember the amazing achievement, on a limited budget, to get us into the Premier League."
Any decision on McDermott's future would be made by owner Anton Zingarevich rather than Madejski, although the chairman does not expect there to be change anytime soon.
"It is Anton's decision as he owns the club, but he has a great affection and loyalty to Brian, and I don't think anyone could consider Brian's position because he has done an amazing job for Reading," Madejski said.
"I am getting fed up with this carping about the manager and this ghastly sort of merry-go-round of managers leaving. It is just not fair.
"If you notice the results, none have been overwhelming defeats. They have been near misses most of the time.
"We are punching way above our level. You have to remember Southampton spent £30 million in the summer, so let's get real. I think Brian is doing the most amazing job."
McDermott is one of the favourites with bookmakers to become the next Premier League manager to leave their post.
The favourite is Martin O'Neill, whose Sunderland side welcome Reading to the Stadium of Light on Tuesday.