Wenger deployed Walcott as Arsenal's lone hitman for the third game running and the move paid off handsomely as the 23-year-old bagged three well-taken goals and set up two more to lift the Gunners back up to fourth position in the Barclays Premier League.
"My desire is to extend his contract. I think he belongs here. Hopefully we can do it," the Arsenal manager said. "I think he loves the club and the club loves him and the reciprocity in love is the most difficult to find."
Walcott's desire to play centrally is thought to be key to his chances of signing an extension to his contract, which expires at the end of the season, and Wenger remains hopeful that the England international will not leave.
Henry, who is training with Arsenal ahead of a potential second loan spell, rose to his feet to applaud Walcott after he broke from the half way line and slotted past Tim Krul to put Arsenal ahead.
A glut of goals then followed. Newcastle equalised through Demba Ba, and Alex Oxlade-Chamberlain then scored to make it 2-1 to Arsenal before Ba grabbed his second to make it 2-2. Lukasz Podolski and Sylvain Marveaux then cancelled each other out with their strikes before Walcott set Olivier Giroud up for both his strikes and he added two of his own - the last one a wonderful chip over Krul after the forward was knocked over by Cheick Tiote in the box.
"Today just typifies what I think he can do through the middle," Wenger said. "The first goal was a Thierry Henry-type goal and he showed great determination with the third.
"He has become a good finisher. He has learned a lot because he is an intelligent player and because he is intelligent he will continue to improve."
Newcastle boss Alan Pardew thought the reason why Newcastle folded so dramatically was because unlike Arsenal, who had their game against West Ham called off thanks to a Tube strike, his team had to play a draining Boxing Day clash at Manchester United.
"I honestly think that would not have happened. We certainly wouldn't have had a scoreline like we had (if Arsenal had played on Boxing Day," said Pardew, whose side now sit three points above the relegation zone.
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