The 27-year-old has fallen out of favour in recent months due to persistent injury problems and the emergence of the likes of Alex Iwobi and Joel Campbell.
With his place in England's squad at Euro 2016 subsequently in doubt, Walcott has been linked with a move away from the Emirates Stadium.
Asked if Walcott could leave, Wenger told reporters: "I don't know yet.
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"I'm not in transfer mode at the moment, but I think he has gone through a bad spell. He has responded very well, because he said: 'Okay, I will work harder and more.'
"Even when he comes on now, you see he is motivated and focused. Let's see how well he finishes the season now.
"You have the emergence of a guy like Iwobi. But the players that did not play [against West Brom]: Santi Cazorla, Mikel Arteta, Mathieu Flamini, Jack Wilshere, Alex Oxlade-Chamberlain, and I forget a few that weren't even in the squad.
"All these players will be frustrated, or the guys who go out will be frustrated. Welbeck didn't play, Campbell didn't play."