Walcott insists he wants to stay at Arsenal and become as big a legend there as Thierry Henry.
Manager Arsene Wenger converted Henry from a winger to Arsenal's all-time leading goalscorer and Walcott, who inherited the Frenchman's number 14 jersey, wants to follow in his footsteps.
He told ESPN: "I want to be an Arsenal legend. Thierry joined the club when he was 22 and I want to become an Arsenal legend like him, playing up front as well, which is a big factor for me. I've played on the right wing and had the opportunity to play up front a bit more so I think it's about time."
Gunners winger Walcott denied his delay in signing a new contract had anything to do with money but admitted agreeing a deal could be a "slow process".
Wenger had warned last week the club may be forced to sell Walcott - something they appeared close to doing this summer - if an agreement could not be reached before the transfer window reopens.
Walcott is seeking assurances of more playing time, especially up front. Talks over extending the 23-year-old's contract, which expires at the end of the season, reached crisis point last month when he rejected a new five-year deal worth £75,000 a week.
It was reported Walcott was holding out for £100,000 a week, but he said: "That speculation on the money side of it has never been me. That's not me. I'm not the sort of person who's influenced by money. I always make my decisions based on football and only football.
"Hopefully, something can be sorted out. I'll just wait for the club to get back to us now and go from there."
He added: "It's a slow process. My last contract took over six months to happen. Hopefully, it can be sorted out. I've never said I wanted to go, I've always wanted to stay."
However, the England star refused to rule out leaving Arsenal completely, saying: "It's one of those things that happens in the game. If it comes to it, if the club had to sell me, I'd be disappointed but, like I said, hopefully something can be sorted."
- Thierry Henry