Wenger is out of contract at the end of the season and the Gunners boss has refused to rule out the possibility of taking charge of England in the future following Sam Allardyce's sudden departure from that role this week.
With Gareth Southgate appointed as England's caretaker coach for the next four matches, there remains an opening the Frenchman could fill when his contract expires at the end of the season.
"Right now my priority is to do well here," Wenger said when asked about the England situation.
"This has always been my club and if I am free one day, why not? I'm focused on my job right now."
Wenger is aware it would be difficult to leave after such a long and successful spell in north London, which has included three Premier League titles and six FA Cups.
"I believe that this club is brave and that's one of the good values of the club and we have shown through the years that we can have a good togetherness at the club and that is always the quality that came out through good and bad moments," he said.
"I think I have one quality which is a passion for the game, and another quality is that I always have the desire to be better tomorrow than I was yesterday.
"If I look back, the way I manage today is not the same as it was five, 10, or 20 years ago. How long can I do? I don't know.
"I rule nothing out because I want to work and I want to do well. I accept that it can finish tomorrow as well.
"It's a love story and you always expect a love story to last forever, but it can always stop suddenly."
Arsenal travel to Burnley looking for a fifth straight victory and Wenger believes they can maintain the momentum from commanding victories over Chelsea and Basel this week.
"We have to go into the game with the same commitment, the same focus that we had in recent games," he said.
"The danger from Burnley comes from the fact that they are very efficient in some aspects of their game, they are very well organised defensively.
"They don't concede many goals at home and they've shown that against Liverpool and Watford.
"They're very dangerous on set-pieces and counter-attacks as well, so we have to prepare well."
Wenger has not escaped criticism from some Arsenal supporters in recent years after failing to win another Premier League title since 2004.
But Burnley manager Sean Dyche believes Wenger's standing should be beyond debate.
Dyche, who will be looking to guide the Clarets to a first win over Arsenal since 1974, said: "As ever they do get people questioning them, but they look a good group to me.
"They've got pace and clever movement, they're very good players. Arsene for me is one of the top managers without a shadow of a doubt. The way he puts a team together, the style, the manner.
"As a manager of course we all understand fan mentality and the thirst and desire to win.
"From a manager's point of view you have to scratch your head to wonder why he's questioned at times."
Burnley, unbeaten at home in three games since the opening day of the season, are likely to be unchanged from their 2-0 win over Watford on Monday, with striker Andre Gray going into the second game of his four-match suspension.