His current deal is due to run until 2016, but talks have been opened in the hope of tying him down past that point.
Giroud netted 22 goals in the 2013/14 campaign, with his efforts helping to secure a top-four finish in the Premier League and a long-awaited trophy in the form of the FA Cup.
The France international claims to be feeling more settled in England after two years at Emirates Stadium and hopes both he and Arsenal can push on again next season.
Giroud told footmercato.net: "I have two years left on my contract but we are in negotiations to extend.
"For now, I am here. There are many great things to do.
"I feel comfortable in the Premier League. My first was not too bad. I had a pretty good second. I hope to do even better (next year).
"I am progressing from year to year, the same as the team."
While Arsenal believe they are moving in the right direction, Giroud concedes that a lack of maturity has prevented them from sustaining a challenge for the Premier League title and that there are issues to be addressed over the summer.
He added: "We were on top for a good half of the season and then we cracked.
"I believe we lacked maturity and that we had a lot of injuries at an important time.
"Above all, we weren't able to adapt to the big teams.
"We have to show progress in these matches, to maybe play less football, but it's difficult because it's our playing philosophy."