La Real are into the Copa del Rey final after their semifinal defeat of Mirandes.
Monreal told Marca: "Winning is always winning, no matter where you are but, when you're at a club like Arsenal, you have to fight for trophies every season.
"They know it's very difficult, but the team is designed for that. Meanwhile, I think La Real [fight for] other types of objectives. It would be a great success to win something here, something special.
"I think I'd enjoy it just as much or [even] more than the ones I won at Arsenal."