The 62-year-old has declared his loyalty to the north London side but the Gunners boss has refused to look beyond the two years left on his current deal at the Emirates
Wenger has been in charge of the Gunners since 1996, winning three Premier League titles, but has seen his side go seven years without a trophy.
"I have two years to go. What is important for me is Southampton and I think I have shown my commitment to this club in the past," he told reporters.
"At the moment I am not in the mood to think about the long-term future. We want to do well this season, that's all.
"I am an Arsenal man. I think I have always shown that. I have to consider if I do well or not. If I don't do well, I have to consider my future.
"I have been at the club long enough to have confidence in the people I work with, but I will assess my own performances and then make a decision, at the moment we are not there.
"Two years is a long time in my job. I just want to do well for the club as long as I can and accept all the rest.
"I have to consider that at my age, you always have to assess if you have the fitness, the desire, the commitment that this job demands.
"Then of course you have to make your decisions. I hope I will be lucid enough and intelligent enough to assess my performance well."
Midfielder Abou Diaby is an injury doubt for Arsenal as they welcome Premier League newcomers Southampton to the Emirates this weekend and Wenger is adamant he will not be risked if he is not fit.
He explained: "Diaby is in a position where we can certainly play him. We just have to assess the risk to play him or not. That will be done tomorrow.
"We won't take a gamble on him, especially because of his history."