Vieira, who is due to be out of contract with the Major League Soccer side at the end of the year, helped Arsenal to three Premier League titles and three FA Cups during his playing days.
Asked about ongoing speculation that he is in the running to return to North London in a coaching capacity, the 41-year-old told The Times: "I know what people are saying, and I'm really happy about that. It's an honour to be mentioned with Arsenal - I love the club.
"I played my best football there and made my name in the game. I am always going to have a deeper relationship with Arsenal. That is not enough to coach that team but I'm ready to coach any side in Europe.
"I don't want this to be perceived that I want to go because I don't want to leave. But, if the question is as simple as: 'Are you ready to manage any teams in Europe?', then I would say: 'Yes. I am ready'."