The Australian, who signed on loan at Arsenal from Brighton in January, has impressed in goals when called upon.
And speaking to Optus Sport, Ryan admitted he believed he was good enough to take Leno's spot.
"Obviously I knew coming here that Arsenal had a great goalkeeper in Bernd, you know, what he's done in his career is a testament to the goalkeeper that he is today and the world-class goalkeeper that he is," Ryan said.
"At the same time, I also have the belief that I'm also a world-class goalkeeper and you know, I felt that I was unsure if I was going to get any opportunities, but if those opportunities were going to come, I was going to show that.
"In order to do that you have to train how you play, treat every session like it's a match and if you're able to do that and the opportunities come around, that's where your confidence stems from, and when the matches have come around I've felt like I've been in a good place and thus I've been able to take advantage."