The Poland international, who has scored 15 goals for BVB this term, will join the German champions on a free transfer at the end of the season.
Despite the arrival of Lewandowski to the Allianz Arena in the summer, Wenger claims that Bayern will not be willing to sell Mario Mandzukic during the January transfer window but hinted that the Croatian's situation could change.
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"Lewandowski is at Dortmund until the end of the season and Bayern will not sell Mandzukic now. Maybe at the end of the season."
As exclusively revealed by Goal in December, Lewandowski was part of a five-man Arsenal shortlist for strikers to target in January, including Atletico Madrid forward Diego Costa, but Wenger concedes that securing a high-profile signing will be difficult before the end of the season.
"All the big players are at big clubs at the moment and they go for important targets," the Frenchman added.
"Unless you have a club in a desperate financial situation, it will be difficult - or if we find someone like [Serge] Gnabry at that age when no-one knows them."