Walcott has just one year remaining on his current contract with the Gunners and, much like Robin van Persie, the 23-year-old could leave on a free transfer next season.
That has led to speculation that the former Southampton winger could be sold this summer, with Liverpool among a host of clubs reportedly interested in signing the player.
But Arsenal are in talks to extend his deal and the England international insists there is nothing to be alarmed about.
"It was always going to be (a case of) hold back until the end of the Euros," Walcott told Sky Sports News.
"We continue to talk and we'll just see where it goes."
Asked if he had been unsettled by the rumours of a move, Walcott added: "Not at all because I didn't have a clue about any other clubs, anything.
"I'm an honest guy. I like to get on with my job. I've got to work on pre-season, I don't want any distractions.
"Like I say, my agent and the club will continue to talk and when there's something to know I'll get involved."
Walcott is about to embark on his eighth season as an Arsenal player and he is determined to repay the faith Arsene Wenger has shown in him.
"The manager has got so much faith in the young players," he added.
"He's developed them. Every single one of them that comes in seems to suit the way that Arsenal play football.
"It's the next step that we need to go on to now. Everybody says that we're a young team but we've got a lot of experience now - Champions League quarter-finals (in 2010) and so on.
"So we just need to try and prove people wrong and show what we can actually do and find out what we're made of."
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