Arsenal are rumoured to have agreed a €14.8 million fee with Montpellier for the striker but the Gunners boss is refusing to talk about the deal, which should be finalised soon
Wenger has acted quickly in the transfer market so far, snapping up Lukas Podolski from Bundesliga side Koln. The future of captain Robin van Persie remains unclear, with the Dutchman having only one year left on his contract.
Giroud could be a replacement for the Oranje striker, or link up with him next season - but Wenger isn't letting anything slip.
"I won't say anything to you," Wenger told TF1. "Even under torture!"
The 25-year-old is set to treble his wages in the Premier League with reports suggesting that he will sign a contract worth over €60,000 per-week.
Giroud netted 21 times in Ligue 1 last season and also contributed nine assists as Montpellier claimed the title despite operating with a budget far smaller than that of rivals Paris Saint-Germain.
Speaking earlier this week, Montpellier manager Rene Girard told French radio station RMC that Wenger was leading a chase of top clubs for the striker.
"Arsenal are very interested and Giroud wants to play in England, if Arsene agrees with the president, he will sign for them," the manager said.