Manager Arsene Wenger says Arsenal will keep fighting for the title as long as it is "mathematically possible".
The Gunners are strong favourites to finish in the top four this season but the Frenchman says his players will keep fighting for something better ahead of the last eight games of the season.
"We have the aspiration to win the next game and that's quite good enough. After that, win the next one," Wenger said on Thursday.
"Whatever is mathematically possible you have to try to achieve but that doesn't depend only on us. What does only depend on us in the final run is our performances and our results, so let's focus on that.
"After that if everything goes for us, you never know, but you can only master your own performances so let's focus on that and be realistic and continue to earn the right to win the games. That's what we want."
Meanwhile, the Frenchman says midfielder Abou Diaby could be offered a new deal at the club if he performs on a consistent basis in the last two months of this campaign.
"By me, yes [a decision has been taken over Abou Diaby's future]," he said.
"I had a chat with him and told him how I can envisage the future. He has to make a decision. Of course he understands completely that he has to perform and to show that he can be present on a consistent way.
"I will see where we go from there. I wouldn't like to go into details, we have to meet again to see where we go from what I told him. It has to be linked a little bit with his presence."