The German forward has been a peripheral figure for the north London club this term and has previously made clear his desire to play more first-team football.
While Wenger has constantly played down talk of the World Cup-winner leaving the Emirates Stadium, Inter coach Roberto Mancini confirmed in the Italian press that Podolski was one of the players he is interested in.
However, Wenger has now dismissed suggestions Podolski could move to San Siro in no uncertain terms.
"That is a joke. Inter Milan is not serious. They talk, there is only talk," Wenger told a media conference on Tuesday.
"He's a player of Arsenal Football Club and I want him to stay.
"Apart from that, what is to be professional is that as long as you are somewhere, you give your best to justify your wages and your love for the club."
Asked whether Podolski would still be an Arsenal player following the transfer window in January, Wenger added: "I hope so, yes."
Meanwhile, Wenger has received mixed news this week with Danny Welbeck rated as doubtful for the New Year's Day clash with Southampton due to a thigh problem.
However, Theo Walcott could feature, having been an unused substitute in the last three Arsenal games due to a recent groin injury.
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