Wilshere reacted to the buzz by tweeting a picture of Zinedine Zidane smoking, alongside the comment: "But for the record....I don't smoke!"
According to British newspapers, a spokesman for Wilshere said he does not smoke, insisting that Wilshere was told by one of his friends to "momentarily hold the cigarette as part of a prank."
Regarded as one of the most promising midfielders of his generation, Wilshere was hampered by an injury last season and is facing strong competition from club-record signing Mesut Ozil.
"I don't know really what happened, I will need to have a chat with him about that," said Wenger, adding he will keep the conversation private. "I disagree completely with that behavior."
It is not uncommon for high-level athletes to indulge in a cigarette from time to time. Former France and Manchester United goalkeeper Fabien Barthez or Zidane have also been pictured smoking during their career, while three-time world player of the year Johann Cruyff was a heavy smoker, and Stanley Matthews featured in an ad for a well-known cigarette brand when smoking was far more accepted.
"Things are different in England especially," Wenger said. "You don't need to convince me (of that) because, I must tell you, I travelled as a football player on coaches after games in France where you didn't see each other, there was so much smoke on the coach. Everybody smoked. But times have changed and the health worry, the example, the role model (expected) from the football players has changed as well."