The defender also believes a third place finish and an FA Cup win represents a successful season for the Gunners.
The Gunners are expected to strengthen again in the summer, with last season seeing them sign Alexis Sanchez and the year before Mesut Ozil.
Sanchez in particular has proved to be a star buy and move Arsenal to the next level, with them finishing third and retaining the FA Cup last season. And Monreal says next season they will be fighting as hard as they can for the title.
“If everyone gives 100 per cent next season, we will have opportunities to win the Premier League,” he said.
“Obviously it will be difficult because there are so many good teams in the league but we will fight for it. I imagine the club will sign new players but at the moment we are making a good group and it will help us for the next season.”
Reflecting on last season, the Spaniard believes it must be deemed a good season after their FA Cup success.
The Gunners beat Aston Villa in the final last month to retain their trophy from last season, and in the process became the most successful team in the tournament’s history.
Add in the fact that they improved on last season’s fourth place with a third place finish, with them at one point looking like a late title challenge could be on the cards, and Monreal can see nothing but positives from the campaign.
“Finishing third and [winning] a trophy means it is a good season,” he added.
“We have to be happy with the team because in January or February we didn’t have a chance to win the league because we were so far away from Chelsea.”