Frenchman Giroud is out until the new year, having had surgery on Wednesday after hurting his ankle in Saturday's 2-2 draw at Everton.
With the transfer window closing on Monday, Wenger says he will be "actively involved" in monitoring potential arrivals, but was not desperate to add to his squad despite losing Giroud, Arsenal's top scorer last season with 22 goals in all competitions.
"I will be actively involved on the final day of the window and I will be on alert until the last minute of transfer deadline day," Wenger told reporters on Friday ahead of Sunday's trip to promoted Leicester City.
"It's harder to buy top, top, top players, yes. Many clubs are on the market and everybody knows each other.
"The last few days are a poker games. There's a lot of lies there in the few days, everybody is interested in the same player even if you're the only one who wants the player.
"(When you are experienced) you can call it a bluff when it is a bluff."
Having splashed out 42.5 million pounds ($70.5 million) on German midfielder Mesut Ozil a year ago, Wenger is not afraid of spending money late, but he is confident his attacking options are good enough to compete even if there were no further arrivals.
"Yes. Why not If I give you the number of strikers I have at the moment it's absolutely unbelievable," he said.
"We have (Yaya) Sanogo, (Alexis) Sanchez, we have (Theo) Walcott, we have (Lukas) Podolski, we have Giroud who will come back during the season and I forget maybe one or two. (Joel) Campbell can play centre forward as well and of course we can be successful.
"The success of a season doesn't depend on one player that you buy or not. I think you do it when you think it strengthens your squad of course (if) you find the right player you want to do it. We have shown in the last two seasons, when we think money has to be spent we do it. But we want to do it in the right way."
Wenger said Mikel Arteta and Kieran Gibbs will miss the Leicester match through injury, while Aaron Ramsey is eligible after being suspended for Wednesday's Champions League second leg playoff victory over Besiktas.