The 23-year-old has been the subject of intense speculation about his future as he and club officials have been unable to agree on an extension to his current deal which ends next year.
British media reports have said money was the contentious issue with Walcott valuing himself significantly higher than the club did.
"I've never said I wanted to go. I've always said I wanted to be an Arsenal player," Walcott said at an English Football Association (FA) "Just Play" event north of London.
"I've never been influenced by the money, it's never been about that. I'm not that sort of person at all. It's always been a football decision for me. If it was about the money, I would've gone in the summer.
"Hopefully, something can be sorted...we're just waiting for the club to come back to us and go from there. Hopefully, I can get back in that team and start playing again."
Walcott said he wanted to play as a striker instead of the wide role he has usually occupied for Arsenal but he has been sitting mainly on the substitutes' bench this season as the team have made an encouraging start.
The high-profile departures of Robin van Persie and Alex Song and a number of new signings in key positions could have destablised Arsene Wenger's squad but they have been playing well.
A thumping 6-1 win over Southampton was followed by a 2-1 victory at French champions Montpellier in the Champions League and Arsenal drew 1-1 at Premier League champions Manchester City on Sunday.
"We've had two very positive away matches against top teams," Walcott said. "I think we could've done better against Man City as well but you've got to take that. We're only going to get better."
Walcott also paid tribute to John Terry, the former England captain, who announced his international retirement on Sunday.
Terry's decision came just a day before he was due to appear before an FA disciplinary committee facing charges of racially abusing Queens Park Rangers defender Anton Ferdinand despite being acquitted in the law courts.
"It's obviously sad to see but you've got to respect his decision," Walcott said.
"Personally, he's been great to me. When I first joined the England team, he looked after me, put an arm on my shoulder, always encouraged me. Great leader, great captain.
"It was an absolute honour and privilege to play with him and he will be missed."
