The Mail on Sunday says the manager is weighing up whether to recommend an £85,000-a-week deal to his board that would break the impasse in contract talks and see the England attacker sign for another four years.
Though Arsenal executive Dick Law would conduct negotiations with Walcott's representatives, he acts on Wenger's recommendations on salaries.
Wenger said: "I don't know how it works at other clubs. But it's not only me: it's in cooperation with the board.
"When I want to go far [in setting a higher salary for a player], I ask the authorisation of the board."