Wenger admires the success achieved by McDermott, a former Gunners midfielder, on a limited budget and believes he has the skill to keep the Royals in the Barclays Premier League.
Last season’s npower Championship winners have yet to win in the league, but are one victory away from a place in the Capital One Cup quarter-finals.
"Reading have made appointments from within the club well over the years," Wenger told Arsenal Media.
"You have to congratulate Brian McDermott for promotion last year, I believe he made a miracle basically.
"When you get to the Premier League, the level of expectation is to stay and I feel they have a chance. McDermott has the qualities to achieve that.
"We expect a challenge and we know Reading will give absolutely everything when they play against us.
"Reading have done very well in their scouting. They are one of the examples of a club not spending money and living within their resources.
"I always respect that. There is some quality work behind their success."
Arsenal’s trip to the Madejski Stadium continues a busy spell that includes Manchester United at Old Trafford on Saturday and Schalke, 2-0 winners in north London last week, the following Thursday.
Wenger will field a blend of youth and experience against Reading as the Gunners seek to reach the last eight of the league cup for a 10th successive year.
"Some players need a breather because they had two international games, Champions League and Premier League games," he said.
"They will have played five games in two weeks. Some will be rested tomorrow. After that I will see after tomorrow night.
"We will still have an experienced side out with players from the squad.
"We will go to Reading with a good team who will have a good chance to win the game.
"We fight as hard as we can to stay in all the competitions and if you have to make a choice you make it as late as possible.
"The Capital One Cup is in a period where you have to make a decision sometimes as it is a time when we also have the League and the Champions League."
McDermott has claimed he is under "good pressure" after Reading’s winless start to life back in the Barclays Premier League.
Saturday’s 3-3 draw with Fulham left the npower Championship winners rooted in the bottom three, their eighth failure to take maximum points from a game this season.
They are level on points with fellow newcomers Southampton, whose manager Nigel Adkins has been forced to endure repeated speculation about his job.
McDermott appears to enjoy more leeway with new Reading owner Anton Zingarevich and insisted he had no fears over his own position.
"I’ve been in this game 30-odd years and that’s something I’ve never ever concerned myself about," he said.
"We’re all working to get the same goal.
"We’re all – absolutely everybody – on the same page."
Claiming he was "relishing every moment of it", he added: "This is good pressure.
"We’re playing in the greatest league in the world, we’re playing in front of a full house, everybody at the training ground is working their socks off to have the best environment that we possibly can.
"You saw the spirit within the group on Saturday against Fulham.
"Any manager in this league or any league is under pressure. We live our life under pressure."
That pressure will be eased considerably if McDermott becomes the first Reading manager ever to beat Arsenal.
The 51-year-old will take on his former club for the first time looking to reach the quarter-finals of the Capital One Cup.
That would pile on the misery for Gunners boss Wenger, whose seven years without a trophy has led many to question whether his own job is safe.
McDermott dismissed suggestions Wenger should be sacked as "nonsense", saying: "It’s never easy when you’re selling your best players.
"[Robin] Van Persie goes, [Cesc] Fabregas goes, and to try to replace those is very, very difficult.
"But he’s got a great knack of finding players. He’s got [Santi] Cazorla, who’s come in and is a terrific talent.
"You’ve got Jack Wilshere just coming back now and (Alex Oxlade-) Chamberlain, who’s really establishing himself.
"I know Steve Rowley, the chief scout there. He’s a really good man and does a great job for them."