The Gunners boss, 64, has yet to sign the offer of a new contract extension past the end of the season, but having just completed 1,000 matches in charge is expected to stay on at the Emirates Stadium.
The Arsenal board is said to be acutely aware of the difficulties it could face when eventually having to replace the Frenchman, with the on-going issues for Manchester United manager David Moyes after following in the footsteps of Sir Alex Ferguson all too poignant.
Wenger, though, stressed he would not be keen to oversee the recruitment process when the time comes.
"I always said, and you can check that, everybody has his job (at the club). My job is to do well for the team, not to do anything else," he said.
Asked if he would be choosing his successor, Wenger insisted: "No."
Arsenal remain relaxed about the on-going saga over Wenger's future, comfortable he will commit for next season, with plans already in place for a July friendly in New York.
It is a situation Wenger also appears completely comfortable with - although again indicated he alone would be the final judge on whether he felt he could take the team on for another cycle.
"My word is my word," said Wenger. Asked if that meant he would definitely be staying on next season, he added: "Yes - unless I decide otherwise.
"I have told you many times we have had no time to sit down and do it.
"(I am) not going anywhere, don't worry for that, but I want to have a feeling coming out of the season that I have done the maximum for the club."
Despite falling behind in the Barclays Premier League title race ahead of Saturday's showdown with Manchester City, Arsenal are in the semi-finals of the FA Cup, which represents a real chance to end their nine-year trophy drought.
Wenger suggested he would reflect on the merits of any success once the final whistle for the 2013/14 campaign is blown.
"Let's first see when the season is over," he said.
"If you look back for one year, would you have done something different? If you say to me 'no', I say 'this guy is a complete lunatic'.
"It is not only linked with the result. It is linked with the situations you have dealt with - have you done well or not?
"Do you ask me 'have I made zero mistakes in the last year?' I am not stupid enough to say 'yes'."
Wenger, meanwhile, remains confident midfielder Jack Wilshere will recover from a hairline fracture in his foot to have an impact for both Arsenal in the final few games and then for England at the World Cup in Brazil.
"It is six weeks minimum. Jack can start rehab. He works at the moment, but to run and kick the ball takes one or two more weeks. He will play for us before the end of the season," said Wenger.