France international Giroud is unlikely to play again until the New Year after undergoing surgery on an ankle injury sustained in Saturday’s 2-2 Premier League draw at Everton.
The injury appears to have left Wenger with limited options up front, but the Gunners boss is adamant he will not be forced into panic-buying a replacement before the transfer window closes on August 31.
"You will ask me straight away who we will buy,” he said. “I give you the answer - at the moment, no-one.
"If you want to make everyone happy, you buy all of these players but what is important is the performance on the football pitch.
“If you look at the players we had on the bench and those out injured, we have players. You cannot buy every time a player is injured.
"We are open for any position as long as we feel the player can strengthen the squad. Buy to buy? I don't see the purpose of that."
Wenger used £35m summer signing Alexis Sanchez as a striker in the Champions League play-off tie against Besiktas on Wednesday, with the Chilean scoring the game’s only goal in a 1-0 win.
Yaya Sanogo, Lukas Podolski and Joel Campbell are other options, while Theo Walcott is close to returning from a long-term injury of his own.
Besiktas manager Slaven Bilic believes Arsenal will struggle to compete in the Champions League without a recognised striker.
When asked if Wenger’s side could go all the way to the final in Berlin, Bilic said: "I would love it because it would make us look like contenders.
"If they improve (they have a chance), and of course they are going to improve, the league just started and they have got a few injuries.
"They are missing the strikers although Sanchez was good tonight. But to win it? With Bayern and Real Madrid? Football is strange but it would be difficult."