Reports in March had linked the 27-year-old with a return to France after he lost his place in the side to Yaya Sanogo.
|4/5||Arsenal are 4/5 with Bet365 to beat Hull on Sunday|
"I have a contract until 2016 and that is what I want. You should not listen to the media."
Arsenal ended their four-game run without a win in the Premier League with a 3-1 victory over West Ham on Tuesday and Arsene Wenger's side are now one point ahead of Everton in the race for fourth place.
"It's better now [at Arsenal]. We are looking for the last four games with much more serenity," Giroud said.
"The main objective is to finish fourth. It's been 17 years that the team qualifies for the Champions League, I don't want to be in the generation that misses it. Champions League is vital for the club.
"The FA Cup final is also an important trophy for the fans, they have been waiting for a trophy for a long time."