Wenger's contract is due to expire at the end of the season and it remains to be seen if he will agree to a new deal.
Some supporters have been calling for the 67-year-old's departure on more than one occasion in recent months following yet another disappointing season, but West Brom manager Tony Pulis claimed this week Wenger intends to stay put.
Giroud has also had his say on his compatriot's future, hoping Wenger will extend his stay in north London.
"We want to see Arsene sign a new deal," Giroud told InfoSport Plus.
"We want him to continue this adventure because we all support him.
"We hope to win the FA Cup this season and qualify for the Champions League again."
Wenger revealed on Saturday he has already made a decision, but is yet to reveal what he intends to do.