The 26-year-old has settled quickly following his £8.5million deadline day transfer from Malaga, helping the Gunners keep clean sheets in victories over Stoke and Sunderland which boosted hopes of breaking back into the top four.
Monreal, who scored his only goal for Malaga in his final appearance last month, told Arsenal Player: "One of the things any player wants is trophies. I cannot complain about my career, but I would like to win a trophy and I hope I can do this with Arsenal."
Monreal, whose first full game for the senior Spain team came after their 2010 World Cup triumph, added: "I am asked to defend well and not so much to score goals. When I go forward and assist others, it is as if I have scored, so that is a great satisfaction for me."
"It is difficult to say what your own qualities are, but I am a committed person and so give 100 per cent in every game. That is the best attribute that every footballer can have, that every Saturday you give everything you have got for your team."
Monreal's arrival to offer competition for England full-back Kieran Gibbs, who is still sidelined by a thigh problem, saw Andre Santos fall further down the pecking order at Emirates Stadium. The Brazilian has returned to his homeland on a loan deal with Gremio.
The 29-year-old was signed from Fenerbache for £6.8million in August 2011, but made just 26 appearances. "I am confident this is the best for both Arsenal and myself," he said on the club's official website, www.arsenal.com. "I just want to say a big thanks to all the people that helped me at this wonderful club."
Santos clearly feels he still can be part of Arsene Wenger's plans in the long-term. Speaking in a separate interview with the London Evening Standard, he added: "The idea is to go there, play well and be able to come back strong. Do I have a future at the club? For sure.
"However, when the club acquired another left-back it was clear to me that I will not play. I need to play, get my confidence back and Gremio is a good platform for this. I talked (with Wenger) and we decided together this would be a good chance for me to get on top of my game.
"He gave me a hug and told me Arsenal would always welcome me back with open arms. He did (want me to stay), but he wanted to see me happy and if I am not performing all the time, then I am not happy."