England international Walcott, 23, is out of contract at the end of the season and talks over an extension have so far failed to reach a conclusion.
Wenger said: "I don't think you can put a time-frame on when it will be resolved. Ideally he has to commit. It is difficult. I believe you have to commit at some stage.
"It is very important in our sport to be very committed to where you are, and as long as you do not do that, you are not completely at ease. It is important for our squad as well that he is completely committed.
"I do not doubt it, but as well at some stage it has to be concrete."
Meanwhile, the Gunners boss admits he is pondering making a move to take veteran striker Henry to the club for a second loan spell from New York Red Bulls.
Wenger added: "I don't rule it out. I haven't made up my mind yet and I haven't even spoken to Thierry about it. I have not completely decided how I will sort it out in my head.
"They (loan deals involving MLS clubs) become more and more popular because their championships are played in a different part of the year. It's good for European teams but I personally believe that football should be played all over the world from January until November.
"Gervinho is going to the Africa Cup of Nations, so we are looking for a striker."