The Gunners have missed out on Champions League football for the past two seasons and last term recorded their lowest finish since 1994-95, a full 12 points adrift of the top four.
However, Mkhitaryan is confident that his side can improve on that under new boss Unai Emery and is particularly looking forward to playing alongside former Borussia Dortmund teammates Pierre-Emerick Aubameyang and Sokratis Papastathopoulos once again.
"It's always nice to play with your old teammates, with Aubameyang and Sokratis. We're all looking forward to the new season and we're going to do our best to help this team reach the top four of the Premier League," the Armenian told reporters.
"I am always in touch with my old teammates, it doesn't matter whether it is in Dortmund, Shakhtar, Manchester... I am in contact with them and it's always nice to talk to them to know how things are going in their lives.
"Of course, when I came to Arsenal and heard they had the opportunity to come here I was just convincing them: 'Come to the club.' Because I knew they would fit in well."
Arsenal's first game of the new Premier League season comes at home to defending champions Manchester City.