Wenger has been in charge of the Gunners for 17 years and the club are in talks to extend his contract which is set to expire in the summer.
The French coach, though, takes no notice of any personal milestones as he looks to guide the Barclays Premier League leaders safely through the toughest of all the Champions League qualifying groups.
"A good game for me is the best present," said Wenger, whose side have won both of their Group F matches so far, most impressively when beating Napoli 2-0 at home earlier this month.
"I get cards, phone calls but, honestly, if nobody reminds me I forget.
"It was always like that. Even when I was 25 or 30, I never thought it as a special day, but people remind you.
"I don't want them (the players) to play (just) for my birthday. I want them to enjoy playing together. If i can enjoy it as well, it is even better."
Wenger has indicated he is willing to pen a contract extension, with negotiations on-going, but shows no signs of slowing down.
"You will see when you are 64, what is amazing in life is that you don't change," he said.
"Also you never believe you are 64, and when you are 50 you don't believe you are 50.
"The only thing that is good is that internally you are still young, externally you become old."
Wenger refuses to be drawn over any specifics on just when a new contract will be in place.
"I want to feel I can do well for this club. It is not a question of my loyalty. It is as simple as that," he said.
"At the minute, I am looking at the short term. I will make a decision about the 'little-bit-longer-term' later."
What is certain is the Arsenal manager's unwavering desire for continued improvement.
Arsenal moved clear at the top of the Premier League with a 4-1 home victory over Norwich on Saturday, when Jack Wilshere finished off a sublime passing move on the edge of the area to set them on their way.
Wenger, though, stressed: "We are always looking for perfection and our game was not perfect. For the next game we do it again what went well and do better what we didn't do well, that's what keeps us going as a manager.
"What is good for me is that after a period of frustration with our fans, we can make them happy again and let the players enjoy the game."
Arsenal will rest midfielder Mathieu Flamini as a precaution following a concussion he suffered during the Norwich match, meaning Wenger must shuffle his side to tackle Jurgen Klopp's well-drilled outfit.
Dortmund will be spearheaded by Poland forward Robert Lewandowski and come into the match second in the Bundesliga a point behind Bayern.
The Gunners take on last season's European runners-up in a double-header on matchday three and four which could well shape the outcome of Group F.
"We are in the most difficult group in Europe," Wenger said.
"If we get out of it we will have a chance to get to the final, but at the moment it is too early.
"The job is in front of us to get out of it.
"We can't be triumphant at the moment.
"We have big targets, big teams and big fixtures in front of us."