The 23-year-old England international capped victory with Arsenal's fifth goal in injury time at the Emirates Stadium on Saturday, having earlier teed up Per Mertesacker for Arsenal's opener.
Walcott is currently in talks about a new contract and has reportedly asked coach Arsene Wenger to give him assurances that he will be given more opportunities to play at the point of Arsenal's attack.
His recent displays have only strengthened his claims and when asked if he still coveted a role in the centre, he told talkSPORT radio station: "Oh, without a doubt. I've always believed I'm a striker.
"The boss gave me five minutes at the end there (against Tottenham) and I managed to grab a goal, which is great.
"But when you've got someone like Olivier (Giroud), who's playing well, there's no need to change a winning team at the moment.
"I think my time will come. I've just got to be a little more patient. But, like I say, I want to play up front. That's my position."