The Sun says they have so far come up around £10,000 a week short, while Walcott also wants to know whether Wenger plans to play him as a central striker.
Walcott is in the last eight months of his contract and will be free to talk to other clubs from January 1.
Arsenal fans are now braced for another exit.
Wenger said: “Yes, fans are fed up. You think I’m not fed up?
“I want our best players to stay. I have discussions every day with Theo but not every day about his contract.”