Jack Wilshere, Kieran Gibbs, Aaron Ramsey, Alex Oxlade-Chamberlain and Carl Jenkinson all committed their futures to the Gunners by penning long-term contract extensions on Wednesday.
Talks over a new deal for Walcott have dragged on for some time and he has been linked with a move away from Emirates Stadium in the winter transfer window, but Wenger has no intention of selling.
Asked if the quintet of contract extensions could break the deadlock with Walcott, Wenger said: "A little bit, I hope."
Questioned on whether Arsenal would sell Walcott, Wenger added: "No, that is for sure. My gut feeling is that he belongs to this club and that I hope he will sign for us. I always am convinced he will stay.
"You never fix yourself a limit on financial restrictions. 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 for the players to make money so 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."