The outgoing 68-year-old bid an emotional farewell to Gunners fans on Sunday as he took charge of the final home game of his 22-year reign.
Frenchman Wenger suggested he has no plans to retire when he leaves the club at the end of the season but said he would attempt to visit north London as often as possible.
“I will cherish every minute I was here but as well it’s a new start for me,” said Wenger. “I would be happy to sit in the North Bank but I don’t know; it depends if I work somewhere else or not or what I do.
Will I, in the job I do, be free on the days Arsenal play? I would be happy to be in the North Bank, if you can offer me a ticket.
A double from record signing Pierre-Emerick Aubameyang, plus strikes from Alexandre Lacazette, Sead Kolasinac, and Alex Iwobi gave Wenger the perfect send-off by securing a 5-0 win against Burnley.
He now faces trips to Leicester and Huddersfield before his lengthy tenure comes to an end.
Wenger, whose departure was announced just over a fortnight ago, said he is still coming to terms with the news.
“I have to deal with that. It is a story that ends,” he said. “And I see it in one way; guys who managed 22 years a club of that stature, there are not many.
So I can only say, my friend, you have been very lucky to have such comfort to work for such a long time for a club of that stature.
Burnley’s hammering in the capital had little impact on their impressive season as they were assured of a place in next season’s Europa League by Everton’s draw with Southampton on Saturday.
Manager Sean Dyche said it was a “massive achievement” for his seventh-placed Clarets to qualify for Europe.
“Burnley Football Club, European football, I don’t think anyone thought that (was possible), certainly not five-and-a-half years ago when I got to the club,” he said.
“I’ve come to understand what it means to a town like Burnley. I’m from Kettering; Kettering’s a similar size. Kettering (football club) nearly went out of business a few years ago.
“For a club like Burnley to be in Europe in any way, shape or form is a massive achievement.”