France international Giroud's future at the Emirates Stadium continues to be shrouded in uncertainty, with reports in the off-season even suggesting the striker was close to joining Everton.
The Gunners have already seen star forward Alexis Sanchez leave for Manchester United this month but are hoping to plug that void by snapping up Borussia Dortmund ace Aubameyang, although Wenger remained tight-lipped over any deal for the Gabon star.
"I cannot tell you more, nothing to announce today. At the moment we stay where we are. It's still possible [something could happen] but we are far from being close," said Wenger.
"We will still recruit someone, it's possible. I cannot tell you more, nothing to announce today. At the moment we stay where we are. It's still possible but we are far from being close."
Image: Arsenal target and Borussia Dortmund star Pierre-Emerick Aubameyang
And while Wenger is keen for Giroud to stay in north London, he admits the exit doors could open up if the club were to add significant quality to their options, although the Frenchman revealed there will be no swap deal with Dortmund over the two strikers.
When asked whether Giroud would be offered up in part of a deal for Aubameyang, Wenger said: "No. I want Olivier to stay, I just told you that if nobody goes in, nobody goes out.
"Maybe one or two young players [will go] out on loan somewhere, [but] the experienced side of the squad will remain the same unless somebody comes in."