The 24-year-old has just returned to action after almost two months sidelined by an abdominal problem which required minor surgery.
Walcott was Arsenal's leading scorer last season, and an integral part of Roy Hodgson's squad as they battled to secure a place at the 2014 World Cup.
With the Gunners top of the Barclays Premier League and the now qualified Three Lions set for a tough group stage against Uruguay, Italy and Costa Rica next summer, Walcott is confident his domestic form can book a seat on the plane to Brazil.
"The first priority is to play well for Arsenal to make sure I am there," said Walcott, who was a controversial omission from Fabio Capello's final squad for the 2010 World Cup, a tactical decision which the Italian coach has since admitted was wrong.
"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."
Walcott told Press Association Sport: "After this little knock, I am back to full fitness, so that is not going to affect me at all.
"I just want to remind people what I can do, I am the best judge of what I can do.
"I am the best judge of myself, so I know I will definitely be right back at it very soon."
Arsenal are certainly in confident mood ahead of Sunday's showdown with Everton at the Emirates Stadium, having recorded a sixth straight home Premier League win when beating Hull 2-0 on Wednesday night.
Walcott - who on Friday visited the Teenage Cancer Trust facility in University College Hospital Macmillan Cancer Centre, which is supported by the Arsenal Foundation - feels the Gunners have the firepower to maintain their good form against the Toffees.
He said: "Everton had a great result against United, but they will be coming to the Emirates to tackle the best team in the Premier League at this moment in time, and with what we have got going forwards, I don't think Everton will be able to deal with that."
The England forward has started on the bench since his return to action against former club Southampton last month.
Walcott, though, is happy to fulfil whatever role is required to help the team achieve their ultimate goal of lasting the distance in the fight for the Premier League title.
"You need to get that balance, and it depends on how it is going, but the boss is so good at that, he has been in the game so long, he knows how to deal with players in position," said Walcott, who was Arsenal's top scorer last season with 21 goals.
"I will play wherever the boss wants me to play, on the right or up front it does not matter to me, we are top of the league, everyone is playing well and full of confidence.
"When things are going well there is probably no point in changing a winning team, because you want to play to the best our your (team's) ability."
The Everton fixture has been designated in aid of the Arsenal Foundation, which will see players and manager donate a day's wages to charity.
The Teenage Cancer Trust Hub is just one of the projects supported by the Gunners, with more than B£1million committed to charities and projects which have helped reach more than 100,000 young people.
Walcott said: "It is so important for us as players to support this charity, we are all donating a day's wages and anything we can do to help lift people's spirit, we are going to grab onto it.
"It is important for us to come to see where the money goes as well, it is nice to be part of it to meet some fantastic people, to see the amount of time and effort which goes into this project."
:: Arsenal's match against Everton is dedicated to The Arsenal Foundation. Arsene Wenger and the first-team squad will donate a day's wages to support a variety of projects that reach young people to transform lives. www.arsenal.com/thearsenalfoundation