The Times says Wenger is looking for a new striker, with Marouane Chamakh, of Bordeaux, Dzeko, of Wolfsburg, and West Ham's Carlton Cole in his thoughts, but will not make a decision until he discovers the prognosis for Nicklas Bendtner.
The Denmark striker returns to the club on Friday, having been treated in his homeland for a groin injury. His recovery date will inform Wenger's transfer activity.
"The real test will be in the next two weeks with the projection on Bendtner," he said. "If he is out for two months, there is no way we can cope. We will need someone, absolutely. We look anyway and if we find a good bargain, we will still do it."