With the Frenchman's existing deal expiring at the end of the season, speculation of a potential summer exit has gathered pace after the 64-year-old has yet to sign a contract extension.
However, when asked if he would be at the Emirates Stadium long enough to register 1,010 fixtures, he told Sky Sports News: "I think so, yes.
"I want to do well, and the expectation level and the impatience is there. My commitment is full. I do not want to look somewhere else. I want to stay here. There shouldn't be any uncertainty at all. My desire is to stay."
Wenger, who joined the Gunners in 1996, has led the club to three league titles - including an unbeaten 2003-04 campaign - and four FA Cup successes.