The Frenchman, who turns 67 next week, celebrated 20 years in charge of the Gunners earlier this month but it is unclear how much longer he will remain the role.
Wenger's contract runs out in the summer when either manager or club could decide it is time for a change.
The England manager's position remains a possibility for Wenger, who admitted he could be tempted by the role "if I am free one day", but he could also sign a new deal to further extend his stay in north London.
Wenger is clear on one thing about his departure, he will not hand-pick his replacement, although he may offer his opinion if asked by the powers that be at the Emirates Stadium.
"I think it is very important in the club that everybody does what he is paid for," he said in an interview with beIN Sports.
"My job is to be the manager of the club and to be responsible for the style of play and the technical policy of the club
The board's responsibility will be to choose the next manager so that is not my job.
"If they ask my opinion, I will give it in an honest way, but it will not be me to choose the next manager
I'm not in their position, I am in my position.
"The love story I have with the club is linked as well with the fact the board has always shown faith in me and I'm very grateful for that.
"No matter what happens, I will have to make my decision, the board will have to make a decision and I will respect the decision of the board anyway, even if I wish to stay on I will respect always the decision of the board - they have the responsibility to do that."
Wenger's passion shows no sign of abating as he goes in search for a first Premier League crown since his 'Invincibles' of 2003/04 won the title without losing.
He welcomes Swansea on Saturday looking for a sixth-straight victory in all competitions and he remains confident in his ability to continually improve his current squad.
"I think I'm moving the club forward, and the way it is managed forward, I'm quite confident on that," he added.
"What will decide me to continue or not is the fact I feel people still want me to be there, the club still want me to be there and my conscience that I have done well or have not done well.
"That will be a decisive factor, have I done well? Have we achieved what I wanted to achieve with this team? That will be at stake.
"Me, purely as a manager, I like to do what I do
Will I do something else one day, I don't know
I'm not at the end of my knowledge or at the end of my desire to do more and become better.
"The only thing that drives me on is that I want tomorrow to be a better manager than today
As long as I have that I don't want to stop my career, even if I don't think I will manage somewhere else maybe."
Any title hopes Arsenal had last season were damaged with a defeat in the corresponding fixture back in March, when relegation-threatened Swansea won 2-1 at the Emirates.
Wenger wants his squad to show on Saturday just how far they have come since then and prove they are bona fide title contenders this time around.
"Last year we had a very negative experience with Swansea who killed our opportunity to win the Premier League," he said.
"We have a good opportunity to show that we have learned from that and that we are capable of dealing with these kinds of opponents.
"That's what is at stake for us
We have to refocus because the players have been away and we've basically had nobody here
We have to show that we can deal with the kinds of fixtures where we are the favourites.
"We were not always capable of doing that last season and we want to show that we have moved forward.
Source : PA