In an exclusive interview with Flashscore's flagship podcast Livesport Daily, Rosicky admitted it was an honour to be linked with the job at the Emirates Stadium, but he has had no offer to take it over following the departure of Edu in the summer.
Since then, Jason Ayto has fulfilled the position and, according to The Athletic, is one of the candidates being lined up for the role.
Others linked include former Manchester United sporting director Dan Ashworth, but Rosicky, who has been leading the sporting side of Sparta Prague since 2018, is an outsider for the role.
Speaking on the podcast, he explained: "The reality is, you could say, simple. My connection with Arsenal is natural because I spent ten years there. And in that time, you form a very strong bond. I have it with Arsenal and Sparta, they are two clubs that I love.
"Just the fact that I am there in some thoughts of the Arsenal management is an honour for me. But I have no offer to go and work at Arsenal."
The former Czech international spent 10 years as a player with the Gunners, making 246 appearances in all competitions and scoring 28 goals.
During that time, he played with current manager Mikel Arteta and the pair have spoken intermittently after what he describes as a "great time" together as teammates.
Rosicky added: "Mikel and I played together for almost five years, I can't say that we are somehow friends and that we have stayed in touch, that's not the case. We were good teammates, I think that whenever we see each other, we are happy. I haven't been to Arsenal for a long time now, during my last visit we spent a lot of time together. But it's not like we call each other."
The trend for midfielders to become effective managers at the highest level has grown in recent years with the emergence of Arteta at Arsenal and Xabi Alonso at Bayer Leverkusen.
Rosicky believes these types of players have an advantage when they leave the pitch for the dugout.
The former Borussia Dortmund player said: "There can be a clear connection there. Arteta, Xavi, Leverkusen's Xabi Alonso, Guardiola... Especially these four. They played in the most strategic place on the pitch, from which you can see everything in front of you, and you have to see everything behind you...
"The situations they have experienced, what angles they see, how you need to play between the lines, how you have to set your body, which foot you pass to, these are the details that they will demand from their players.
"They have experienced it on the pitch. That can play a huge role in why they are such successful coaches. They have an advantage in that they experience certain situations directly on the pitch and can pass it on to the players."
Under Rosicky's leadership, Sparta Prague lifted the Czech league title for the first time in nine years in 2023, and backed that up a year later with a second successive league victory.
This year, they are off the pace of rivals Slavia Prague and currently sit third in the standings.