Midfielder Alex Song completed his move to Barcelona on Monday, following Manchester United new-boy Robin van Persie out of the Emirates Stadium.
Wenger is keen to add Nuri Sahin to the squad as a replacement for Song and is also hoping to sign a defender before the window shuts.
"We are looking to bring one more midfielder in of course, and maybe one defender as well because we still feel we are short in some positions," he told Arsenal's official website.
Wenger watched on as his team struggled to hit the net against Sunderland on the opening day, drawing 0-0 in front of their own fans.
And the long-serving boss is at a loss to explain his team's inability to beat the Black Cats.
"We didn't lose, but it is frustrating when you are home with everyone here and you do not create more chances than we did," he added. "It is very difficult to understand."