The England forward is currently in negotiations with the club over a new deal, as his current one expires in the summer. While there is yet no swift conclusion on the immediate horizon, Wenger - who maintains the player will not be sold in the January transfer window - remains confident Walcott will eventually commit his future to the club he joined as a raw teenager in 2006.
"My gut feeling is that he belongs to this club and that I hope he will do it and sign for us. I always am convinced that he will stay," said Wenger.
Walcott was deployed in his preferred central striker's role at Reading on Monday night, where he netted the final goal in a 5-2 win which lifted the Gunners back up to within two points of fourth place in the Barclays Premier League ahead of this weekend's trip to Wigan.
Walcott is said to be determined to prove himself at the spearhead of Arsenal's attack, with Wenger having often deployed the England international as an impact player from the flanks.
The club and player's representatives are understood to still be some way apart on wages, with terms of around £75,000-per-week offered while Walcott is seeking a package of up to £100,000.
When asked whether he felt Walcott was worth such a vast sum, Wenger maintained it was not just a simple numbers game.
"I never see football like that. You never fix yourself a limit on financial restrictions," he said. "At the end of the day, can you pay what the player wants? And does it fit with your wage structure?
"I have always fought that the players make money, so therefore I am happy when the players make big money, but it has to be made possible for the club to pay it. I believe the board will follow my recommendation, if it is possible.
"We have a wage bill that has to be respected. When we go overboard and higher than it is expected, I ask the board to do it and most of the time they follow my demands."