Walcott, playing on the right wing in Arsenal's 4-2-3-1 formation, scored the second hat-trick of his career to help put his World Cup disappointment behind him and was a constant menace to the promoted side.
Though he has attracted criticism at times for his performances on the wing, and has scored only 12 goals in five Premier League seasons, Wenger expects Walcott to emulate his predecessor in the No. 14 shirt, Thierry Henry, by adopting more of a central position in the years to come.
"You always worry about a player's development, but I was always positive about Theo because I have looked at his disappointments, and how well he analyses things," Wenger said.
"When you are intelligent, you always improve. He's not there yet but he is developing, maybe what happened to him is part of his development.
"I believe he can score goals because when he was young he scored goals, and I am convinced he will finish in the middle. He times his runs well, once he is a yard clear nobody in the world can catch him, and now he is more composed in front of goal."
Walcott says he is honing his skills as a striker in training and would be happy to perform in the role if required by Wenger.
"The boss signed me as a striker but I'll happily play anywhere for Arsenal," Walcott said. "There's a lot of competition up front now with Marouane [Chamakh] and Robin [van Persie], so as long as I provide goals and pop up with one now and then I'm happy with that.
"But if the boss wants me to play up front I'm buzzing from that. I'm working in training up front so I'll go from there."