The France striker, thriving in his second season at the Emirates with 20 goals in 46 appearances, says he is happy at the club despite their faltering title campaign and wants to extend his contract beyond its current end in 2016.
Wenger's contract, meanwhile, expires at the end of this season and Giroud hopes his boss signs the deal that has been on offer since the end of last year.
He said: "Of course I will be at Arsenal next season. I am happy in London.
"I have a contract until 2016. Why not extend? I'll still be a Gunner next year - at least I'd like to be.
"I want Wenger to stay at Arsenal next season. Of course we want him to extend his contract. We need him and his experience - he has to stay.
"I think we can compete for the title next season and this time all the way to the end."
The Gunners looked on course for a shot at a first Premier League trophy since 2004 when they topped the division in early February, but a run of only three league wins since then has seen them drop to fourth.