The 27-year-old has enjoyed a strong second season for Arsenal, scoring 20 goals in 47 appearances in all competitions.
And although Arsenal's Premier League title bid has fizzled out, Giroud is determined to stay at the Emirates Stadium.
He said recent speculation about a move was just that and that he hopes Wenger - who is out of contract at the end of the season - also commits his future to Arsenal.
Giroud told French TV station TF1: "Could I extend my contract? Why not?
"You shouldn't listen to that (speculation). A lot of things were said. I'm still happy in London and with Arsenal and think I will be in the future.
"I have a contract until 2016 and I'm an Arsenal player. I want to be here next season, at least that's my will.
"Of course we all want him (Wenger) to continue the adventure.
"I'm sure next season we can challenge for the title - I hope, right until the end of the season - and we need the coach. We need his experience. He has to stay.
"Things are better, we've got a bit of serenity back with regards to fourth. I would say the main objective is to finish fourth - we know that the Champions League is a vital objective for the club.
"We've played in it for the last 16 years and I don't want to be part of the team that misses out. But the FA Cup final is also very, very important for the club."
Arsenal sit in the fourth and final UEFA Champions League place, one point above Everton with three matches to play.
