The Gunners have won just two of their seven Premier League games this season and face fellow strugglers Sunderland at the Emirates next Sunday.
Walcott said: "You've got to play well for your club and the manager will pick players on form, so I'm not going to look too far ahead after what happened to me a couple of years ago.
"He plays players in form and you always get a chance to play and show what you can do and hopefully we can take that into the tournament when it comes to it.
"Firstly I'm going to be concentrating on Arsenal after the poor start we've had.
"But it's great to have qualified with England - and the fans were great in Montenegro even when we went to 2-2. This shows what it means to them."