The Frenchman's contract with the Gunners is due to expire in June and he repeated his statement from Thursday, given to German television, that he would decide his plans "in March or April".
Calls from fans for the 67-year-old to leave after over 20 years in charge have intensified following the midweek 5-1 UEFA Champions League mauling at Bayern Munich.
But, after making an impassioned defence of his time at the club, Wenger said he had no intention of retiring.
He told a news conference ahead of Monday's FA Cup fifth-round tie at non-league Sutton United: "I am used to the speculation over my future. I have been here for 20 years. But no matter what happens, I will manage next season.
"Regardless of whether it is here or not, it is for sure that I will still manage. In life, it is important to do what is right. If I said that I will make a decision in March or April, it is because I did not know. I speak to the board but I do not want to talk about how they view my future. My future is not important, the team and Arsenal are important.
"There is always debate over whether I should leave after a disappointment. It is important for the club to make the right decision for the future.
"I did not work here for 20 years not to care. I had many opportunities to go somewhere else but I care for this club and its future. It is important to be in safe hands."
On his time in North London, which has seen Wenger win three Premier League crowns and six FA Cups, he said: "I hate defeat, I hate to lose games. I have a big responsibility at this club. It is difficult to take but I have the strength and experience. I am in a public job and I must accept that. Everybody can have an opinion.
"But even if I leave, Arsenal will not win every game. Let's not forget Arsenal did not play a lot of Champions League games before I arrived. It is not like Arsenal won five European Cups. They never won it. We have to take things in perspective.
"As long as you don't win everything, there is always something wrong. You have to accept that.
"In the last 20 years in Europe, only three clubs have played every season in the Champions League - Arsenal, Bayern Munich and Real Madrid. If everything is not perfect, not everything is wrong."