The 25 year-old is now in his second season with the Championship club and admits he has an eye on joining his former Denmark youth teammates in the senior squad.
Madsen was part of an exciting Danish generation as he was capped at each youth level, playing alongside the likes of Rasmus Hojlund, Gustav Isaksen, Morten Hjulmand and Matt O'Riley.
He told Tribalfootball.com: "Yeah, I hope I can (join them), of course.
"But I think, when I look at my last season, then I also need to be, of course, self-critical and also realistic and I didn't show my real level.
"I wasn't consistent, but I ended pretty well the final six games at the end of the season.
"Now the target is to start well and perform every week and then if it comes (Denmark selection), it comes."
Madsen added, "But I also need to be realistic. There's some really good players in my position, either captaining Sporting Lisbon (Hjulmand) or playing in Genoa (Morten Frendrup), playing in Marseille (O'Riley), so that's difficult competition, but I believe that I, at some point, will make it to the national team."
Personal improvement
Madsen is confident there's plenty of room for improvement in his game and says QPR and the Championship can accelerate his development.
He continued: "My personal hopes are to be a contributor on the team. Being someone who takes a lot of responsibility. Also, I want to show what I can do on the ball, make an impact there, but especially also show that I actually can defend and I actually can run and play a big part defensively as well.
"So I think (with QPR) I can become a complete midfielder."
Successful in Belgium with Westerlo before his move to QPR last year, Madsen admits the demands of the Championship have been a major learning experience.
He said: "I do need to be more calm on the ball.
"For example, you're getting pushed by the fans or whatever... I think that's the biggest difference. Also there's big momentum shifts in the game where you can be on top for 25, 30 minutes and then you can be completely under pressure in the next 30 minutes.
"So, I think that's what is the biggest difference, yeah, in terms of playing (here)."
Gerrard admiration
While admitting he didn't grow up idolising any major star, Madsen says he did admire Steven Gerrard given his family are all Liverpool supporters.
"My whole family are (fans), so I watched a lot of Liverpool games, of course, with Steven Gerrard back then.
"So, yeah, he was someone I looked up to. Because of his abilities, but also what I wanted to learn was how he was expressing himself.
"I don't think I'm completely there, but I think I've understood more now, especially with one year in (England) and learning not just what it takes, but what is important for the fans and what is important to play for QPR and in the championship."
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