The former Arsenal captain and France international told Britain's The Times in an interview that he was "honoured" to have his name mentioned among the possible candidates to succeed Arsene Wenger as manager.
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However the 41-year-old repeatedly emphasised that he was enjoying his role with New York, who are owned by the same parent group as Manchester City and are currently top of the MLS Eastern Conference.
"I mentally know what's going on, what people are saying," Vieira told The Times when asked about the speculation linking him to Arsenal. "I'm really happy about that because I think it's good to have your name linked with a team like Arsenal. But honestly it's not something which will stop me doing what I am doing at the moment."
Vieira was a cornerstone of Wenger's first decade at Arsenal, and was captain during the Gunners' famous "Invincibles" unbeaten season in 2004.
Wenger confirmed last week that he was leaving at the end of the season after 22 years in charge of the Premier League giants.
Vieira said that while he had a special relationship with Arsenal that alone would not prompt him to return to England.
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"It's an honour to be mentioned with Arsenal," said Vieira. "It was somewhere I spent nine years and 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 (alone) is not enough to coach that team but I'm ready to coach any side in Europe.”
However, the Frenchman played down the links. "I don't want this to be perceived that I want to go because I don't want to leave,” he said. “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. I think we're all doing this job because one day we want to coach the biggest teams in Europe.”
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