Arsenal currently occupy sixth place in the Premier League table, some eight points off London rivals Chelsea in fourth, leading to suggestions that winning the Europa League may be Arsenal's most realistic was of qualifying for nexy season's Chempions League.
However, the Armenian isn't giving up hope of overhauling Antonio Conte's side, insisting that "naything is possible".
"Of course, it [Europa League] is very important, but I wouldn't say we stop ourselves from saying we are going to compete in the top four," he told 'ESPN'.
"We are still in the competition because in the English Premier League anything is possible.
"Maybe sometimes, teams can lose two, three times in a row and we win our games so anything is possible.
"We are trying to win every game in every competition and, of course, we will be glad if we can win the Europa League as well, but if we can be in the top four, it will be even better."
Mkhitaryan won the Europa League with Manchester United last season and admitted that the potential for back-to-back titles motivates him hugely.
"It's always a pleasure to win trophies and it will be even better to win twice in a row," he explained.
"It's not easy as you see there are a lot of good teams in this competition; we have to fight in every game, every minute to show up that we have to win that."