The England forward says Arsene Wenger's side are also looking to be competitive in the Champions League after disappointing last season.
The Gunners are being tipped as potential challengers for the crown in 2015/16 after winning their second successive FA Cup last term and enjoying a productive run in the league over the second half of the campaign.
They have also added Petr Cech this summer, with many saying his addition in arguably their weakest area has pushed them even closer to being title contenders.
And Walcott says competing on that front is a top priority, although they are also keen to impress in the Champions League after suffering a disappointing exit to Monaco last season.
“A lot of our priority this season is to challenge for the Premier League,” he told arsenal.com.
“Lastly we want a good Champions League run, we were disappointed last season when we went out but our main target is the Premier League. That is our biggest goal.”
FA Cup still a target
The Gunners have enjoyed a solid pre-season this time around, with victories in tournaments such as the Barclays Asia Trophy and the Emirates Cup having helped to raise anticipation levels.
They also defeated Chelsea in the Community Shield on Sunday, another significant victory as it was Arsene Wenger’s first over arch rival Jose Mourinho, ending that particular hoodoo.
And Walcott says that the vibe in the dressing room is one of wanting to compete on all fronts, with the retention of the FA Cup considered to have been a big achievement and a triumph they would like to experience again.
“The vibe in the dressing room is that we want to do well this year,” he added.
“Retaining the FA Cup is a big achievement and we want to do that again.”