Since Arsene Wenger's shock announcement on Friday, Vieira has been touted as a potential replacement at the Emirates.
However, the New York City coach has now appeared to distance himself from the Arsenal job.
"I spent nine years at Arsenal which makes the club really special for me," Vieira told New York radio station WNYE.
"But that is not enough to coach the team."
Vieira continued: "I am always flattered to hear my name linked with different football clubs.
"That is good for your ego but at the same time, I am happy here.
"We will see what will happen in the next couple of years."