Wenger is reported to be ready to sign a new two-year deal after revealing at the weekend he had made up his mind regarding his future and that an announcement would be made "very soon".
While the Gunners were eliminated from the Champions League and are all-but out of this year's Premier League title race, they have reached the FA Cup semi-finals, where Manchester City await.
France striker Giroud, who has joined up with his international team-mates ahead of games against Luxembourg and Spain, wants Arsenal to win the cup and persevere on with Wenger in charge.
He told Canal Plus: "We want Arsene Wenger to renew his contract, to continue his adventure, because we support him. We hope we can win the cup and that Arsenal qualify for the Champions League."
Meanwhile, it is understood that, contrary to reports from German newspaper Bild, Arsenal have not made an approach to Borussia Dortmund coach Thomas Tuchel and seem resolved to stand by Wenger.