The Gunners are hunting for fourth place in the Premier League table alongside Tottenham Hotspur and Everton.
"We are very confident [of finishing in the top four]," the Irish Independent quotes Walcott as saying.
"We can battle through any sort of situation. The teams around us are winning as well, but we have just got to make sure we look after ourselves and try to win as often as we can."
The Gunners currently sit four points behind fourth-placed rivals Tottenham.