Wenger will reach the landmark in Saturday's Premier League title clash at Chelsea, but the club are yet to confirm details of a new deal for their long-serving boss.
Speculation that Wenger could leave in the summer was quickly countered by the Frenchman, who is confident about extending his lengthy reign.
Asked if he would still be at Arsenal after 1,010 matches, Wenger replied: "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 does not want discussion about his future to serve as a distraction in the crucial closing weeks of the campaign.
"It will be done soon, but I want now to focus on the end of the season," said Wenger, whose side could close the gap on leaders Chelsea to just a point with a game in hand and are through to the semi-finals of the FA Cup.
There has been radical change at Arsenal since Wenger took charge, with the manager playing an integral role in the move to their new 60,000-seater home at Ashburton Grove.
Arsenal are yet to bring any silverware back to the Emirates, but Wenger disputes claims that the club has stood still since the departure from Highbury.
"In 2006, we were in the Champions League final. Nobody speaks about it now, but it is still an achievement," he said.
"It is not a trophy, but we did without conceding a goal in 10 European games and we only lost in the last 13 minutes of the Champions League. Can you say you have failed that season? I don't think so.
"We beat Real Madrid (in the second round) with Zidane and Beckham and all those players, on top of that we managed to stay in the top four (of the Premier League) that season, but nobody speaks about it. It is like we did nothing that season at all.
"Why? Because at the end of the season we don't parade with a trophy.
"If we had won the League Cup that season people would have said 'they won the League Cup in 2006', but what is that compared to going into the Champions League final without losing a game?
"You have to take a bit of distance with that and assess what is difficult and what is less difficult.
"I know trophies are important, but if you don't have a trophy it doesn't mean nothing happened in the season and you have been disastrous - in a season where you win trophies, you still have bad games."