The Frenchman watched on at the Emirates Stadium on Sunday as his side eased to a 1-0 over West Brom, courtesy of Olivier Giroud's 16th Premier League strike of the season.
Wenger fielded questions over his future after the match – which was Arsenal's fourth league win in a row – and re-iterated his desire to stay at the club.
The 64-year-old is yet to sign a new long-term deal reportedly offered by the club but said: "My last time will come.
"You'll get rid of me one day, don't worry.
"My word is my word and I'm from a period when you didn't need a pen to commit.
"If I had moments of doubt they would have been a few years ago when I had to say no to many offers and I committed to this club under a lot of pressure."
Wenger also took time to discuss the future of full-back Bacary Sagna, who was encouraged to stay by fans at the end of Sunday's match.
"I want him to stay and I hope that convinced him that we want him here," he added.
"We have two players at the end of their contract, Sagna and (goalkeeper Lukasz) Fabianski, and if it's down to me they both stay."
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