Walcott told the London Evening Standard: "He can have a big part to play in our season, without a doubt. It's a great thing at this club that we have a lot of competition for places now.
"Thomas wanted to prove a point and I'm sure the way he played against Chelsea, he is definitely in the manager's thoughts now.
"I'm very happy for him, he was fantastic and helped get us a clean sheet and that will give him a lot of confidence. Thomas will want to make that position his own."