The 19-year-old, who has made a bright start to his Bundesliga career after being drafted in for the injured Rafael van der Vaart, previously remarked that the Gunners were "interesting".
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"We will assess that situation in January," the Arsenal boss told the press. "At the moment we are, like every club, focused on the short term and, for us, what is vital is [Saturday's] game [against Manchester City].
"On the transfer market, usually January is more talks than concrete signings."
Asked specifically about Calhanoglu, Wenger replied: "All the agents will turn up with names. Many agents have good links with newspapers. The names turn up but that is not true.
"If you look well, even the clubs who struggled not to go down, even those who bought a lot [in January], you realise it does not help a lot."