Walcott's current deal expires at the end of next season and Liverpool have been linked with a move for the England forward.
Wenger recently stated that he is expecting contract negotiations to be a long-drawn affair, saying Walcott is "very quick on the pitch, but off the pitch not always".
Walcott on Thursday moved to clarify his situation, denying reports that all is not well between himself and Arsenal boss Wenger.
He tweeted: "I don't normally comment on false stories about myself but reports about contract demands & bust-ups with the boss are complete nonsense.
"There have been no contract talks as yet and my current focus is not on contracts but on doing my best for Arsenal FC."
The former Southampton man has started just five games for the London club this season after recovering from a serious knee injury.
