The England international says the team is full of belief after going on a strong run and feels that Aaron Ramsey is "like a new signing" after scoring six goals already this term
The Gunners beat Marseille 2-1 in the Champions League, to make it 10 straight wins away from home, and Walcott feels the run proves the quality of the current squad.
"We've got players who are playing fantastically well," Walcott told reporters. "There is so much belief in this team at the moment and I think it's showing. We just need to push on and make sure we get that home form going now; the away form is absolutely fantastic.
"We've got to stay fit, which is crucial – we don't want to lose any more players. But as soon as the players come back there is going to be more competition for places and that's only going to be a good thing for Arsenal. I think we'll push on and we can definitely challenge [for trophies] this year, for sure.
"Someone told me in the dressing room it's 10 successive wins away from home – it's a record. To be part of a team that has done that, in the amount of years that Arsenal have existed, is a great honour and a great achievement for everyone. It just shows how talented these players are.”
Wednesday’s victory in France saw Aaron Ramsey bag his sixth goal of the season, and Walcott was full of praise for the Wales international who had been in impressive form so far this season.
"It always takes time when you have injuries and [Aaron] had one of the worst injuries in football," he added.
"He's worked really hard and it's definitely paying off now. He's enjoying his football, he loves touching the ball and he's got something different to his game now which is goals.
“People would criticise that side [in the past] but I see him in training every day and he's looking a totally different player. He's like a new signing. It's an absolute honour to play with him at the moment."