Arsenal chairman Sir Chips Keswick issued a statement last month claiming the board were aware of fan pressure against Wenger, and said a decision over his future would be announced in due course.
The Times says Wenger thought the comments didn't carry enough clout, and should have been made by Ivan Gazidis, the club's chief executive, or majority shareholder Stan Kroenke.
The veteran French manager is also said to be annoyed about backroom changes being made by Gazidis.
The executive is planning for the future by shaking things up behind the scenes, including appointing a director of football.
But Wenger is resistant to the change.