Wenger expects Walcott - out of contract this summer - to put pen to paper by the end of this month.
He said: "I am optimistic we will get to a happy conclusion. Theo is 23-years-old. For a striker, he's coming into the best age now.
"If you compare Theo from today with three years ago, he is a different animal. Today he finishes in a calm way and very accurately."