Van Persie is set to join Manchester United in a £24 million transfer on Friday and Thomas Vermaelen has already been named as his replacement as Arsenal captain.
Song, meanwhile, is a target for Barcelona and it is reported that a £15 million deal could be close to completion.
Wenger is notoriously reluctant to discuss transfer business but in his press conference on Friday said Song leaving Emirates Stadium was a real possibility.
Arsenal have been linked with Real Madrid midfielder Nuri Sahin as a potential replacement for Song, initially on loan, and Wenger says new signings are possible.
When asked about Song's potential exit and new faces coming in, Wenger said: "Both can happen."
"This decision (on Song) is not made. No (bid has been made). I cannot tell you more."
The Arsenal manager added: "Midfield is a different area because we have nine or 10 midfielders of top-class quality. 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."
Song joined Arsenal as a 17-year-old in 2005 and while his contract currently runs until 2014 it has been suggested he is unlikely to renew it.
- Thomas Vermaelen
- Manchester United