The 27 year old joined the Gunners from Malaga in January and believes that the squad is good enough to end their eight-year quest for a trophy.
"I would not just say one trophy, I would say a few," he told the club's official website.
"Of course that is very tough to achieve. The Premier League is very difficult, the Champions League, these are major trophies but we are on a good run.
"We are top of the table, it is still early doors, but we will take every game as it comes and at the end hopefully we'll win a title."
Monreal also said that Arsenal's table-topping form shows that he chose the best time to join Arsene Wenger's side.
"When I was offered the chance to come here, I was in the best moment of my career," he added.
"I had a lot of confidence, I had Manuel Pellegrini's trust, I played a key role at Malaga and with the national side, and I think I came here at the right time.
"We have a happy group and that is very important to playing football well."