The 24-year-old has been out for the past two months with an abdominal injury he sustained in September and is in line to return for his side against Everton on Sunday.
Walcott told Sky Sports News: "The first priority is to play well for Arsenal to make sure I am there.
"It is healthy to have competition [for places], we all want to see English players playing really well.
"I bounced back from the disappointment of 2010 with a very good season for Arsenal, and then last season I finished as top goalscorer, which was a massive personal achievement."
Arsenal are currently top of the Premier League after 13 games this season.