As exclusively revealed by Goal, the England star was ruled out of the 2-0 win over Liverpool after suffering a recurrence of his long-running ankle problems which have see him sidelined for Wednesday's game against Jurgen Klopp's side.
"Jack Wilshere has not travelled," Wenger told the pre-match press conference. "He has another test on Thursday if he does not pass that he is out for Sunday and for England.
|15/2||Olivier Giroud is 15/2 with PaddyPower to score in an Arsenal win over Borussia Dortmund|
The Premier League leaders go into the game level on points with Dortmund but having lost 2-1 to the Bundesliga side at the Emirates Stadium in their last meeting and Wenger is looking forward to the return fixture.
"We are a positive side, Dortmund are a positive side so you have a guarantee both sides will try and win the game," he added. "We lost the first game because we wanted to win it. We got caught on the counterattack because we were not happy with the draw."
Robert Lewandowski was the match-winner for Dortmund in north London, scoring a late winner to secure victory for the visitors, and Wenger is well aware of the danger he poses.
"Usually, at home, Lewandowski is quite dangerous," the Arsenal boss observed, "but the best way to keep him quiet is for us to have the ball."