The former Barcelona man, along with Mesut Ozil, has under 18 months remaining on his current contract and is understood to be stalling on recommitting over issues such as Arsene Wenger's future and their own pay.
The Chilean, in words that mirror that of Ozil's from Sunday after being named German player of the year for a fifth time, says he is "comfortable" at the club and wants to repay their fans' faith with silverware.
"I definitely feel like an important player, and my team-mates let me know every day," he told Arsenal's official YouTube channel. "I try to prove that I am an important player every day and game after game.
"I believe we have the players and the quality to win many things. I feel really happy and comfortable at the club. I want to give the fans a new title.
"We always get our fans' support in the thick and thin, which is great. We must win the Premier League or Champions League for them."
Ozil seemed visibly upset after being substituted during Arsenal's dominant 4-0 win at Swansea City, sitting on the bench with a coat over his head as he watched the final 11 minutes of the game.