Wenger has become accustomed in recent years to Arsenal supporters and pundits calling for him to resign and the Frenchman was under-fire again last week after three successive defeats dealt a major blow to the team's Premier League title challenge and Champions League campaign.
Arsenal legend Thierry Henry claimed he has never seen the club's fans as angry as they were after a home loss to Swansea, while former Liverpool boss Graeme Souness called the Gunners "weak and insipid" and claimed they "bordered on a joke" during their defeat to Manchester United last month.
Wenger, who is now the longest-serving manager in Europe as he approaches 20 years at the helm at Arsenal, takes his side to Hull in an FA Cup fifth round replay on Tuesday as they look to win the competition for a third straight season.
Asked if the way fans react to him over the remainder of the season would affect his thoughts over signing a new contract at Arsenal, Wenger made it clear he had no interest in what the doubters say.
"Look, I have worked here for 19, 20 years and I'm always sitting here having to justify that I'm good enough to do the job," Wenger told reporters on Monday.
"I have no problem to cope with everything but I find that a bit boring in the end. I always have to convince you that I am good enough. I worked for 35 years at the top level.
"What I find just boring is always sitting here after 19 years to face: 'Do you think you are good enough?' If I am not, somebody will tell me."
While Arsenal haven't won the title since 2004 and reached their only Champions League final back in 2006, Wenger is adamant he will go about his job of trying to deliver those trophies rather than focusing on what he cannot control.
"I cannot influence the behaviour of the fans. How can I do that?" he said.
"I am humble enough every day to question myself, to accept my mistakes, and believe me I do that. After that as well there is no coincidence that the people who own the club tell me to be here for 19 years. Do you think they are more stupid than you or me?
"I am not on Twitter. I don't invite anybody to go out to dinner and be nice with them. I work and work and work and work. If it's not good enough someone will tell me one day."
First Published On : Mar 8, 2016 12:47 IST