The Cameroon midfielder has been linked with a 15-million-pound ($23.5 million) move to Barcelona.
When asked if the 24-year-old could leave and others come in, Wenger said: "Both can happen. This decision (on Song) is not made. No (bid has been made). I cannot tell you more."
Even if Song moves, Arsenal has a large group of capable midfielders.
"Midfield is a different area because we have nine or 10 midfielders of top-class quality," Wenger said. "Just today we have six or seven midfielders available, plus (Jack) Wilshere and (Emmanuel) Frimpong who are coming back. (Abou) Diaby is available again, (Mikel) Arteta, (Santi) Cazorla, (Aaron) Ramsey, (Alex) Oxlade-Chamberlain now plays central midfield -- this is an area we have much more freedom to make decisions."
Wenger confirmed central defender Thomas Vermaelen would be the club's new captain after van Persie's departure. The Holland international is in the process of finalizing the formalities of a switch to Manchester United, having earlier in the summer announced he would not be signing a new deal with the Gunners.
However, the Arsenal manager is confident Belgian center back Vermaelen can lead the club forward.
"Vermaelen was vice captain, so it is a quick decision," Wenger said at Friday's news conference ahead of the Premier League opener against Sunderland. "I think we have many potential captains, and Mikel Arteta will be the vice captain."
"We regret that we have lost a great player and for one simple reason -- he only had one year left on his contract. He wanted to go," Wenger said. "We anticipated this situation might happen, therefore we bought Podolski and Giroud. I think we were prepared to keep him of course, but as well the worst (case scenario) was to sell him.
"Selling to a rival was not what we wanted, but there was not much choice. "We had only one club really interested at the level we thought would be acceptable and that was Manchester United. At the end of the day, that was the only decision we could make."