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."