McDermott has come under increasing scrutiny following four successive defeats, the latest a 1-0 loss against Southampton.
However, Madejski says the speculation is "totally absurd" and has given McDermott his full backing.
"It is totally absurd that the manager will not be with us this time next week," he said.
"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, but Madejski does not expect any changes.
"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 £30million 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 leading contender is Martin O'Neill, whose Sunderland side welcome Reading to the Stadium of Light on Tuesday night.
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