Walcott's contract expires at the end of the season and is free to speak to other clubs from next week.
But Wenger said: "My desire is to extend his contract. He belongs here and hopefully we can do it.
"Should he have had a disastrous game today, it would not have altered my determination to extend his contract."
Arsenal 7-3 Newcastle: Theo Walcott coy on future despite hat-trick
Sharp-shooter Theo Walcott
Theo Walcott, who has scored 10 goals in his last 10 appearances for Arsenal in all competitions, has scored with 35.8% of his shots this season in the Premier League - the best ratio of any player to have scored five or more goals
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