The Germany international has become a peripheral figure at the Emirates Stadium this season as Alexis Sanchez has shone since his arrival from Barcelona.
With Alexis and Podolski playing in similar positions it has been the 29-year-old who has missed out, only making four substitute appearances in the Premier League.
The World Cup winner has hinted he may have to depart in search of first-team football, with Napoli reportedly eyeing a January deal, but Wenger is keen to keep hold of Podolski.
"It is not established at all that he will leave at Christmas," Wenger told beIN Sports. "It is me who sets the price and [the reported deal] doesn't correspond at all to his price.
"He is not for sale and there is no offer.
"Podolski plays a position where there is a big competition. He came very late from his holidays [after the World Cup in the summer], so he started after his team-mates and was not good physically."
In all competitions Podolski has made seven appearances this season, with his only start coming in September's League Cup defeat to Southampton.
