The 17-year-old Georgian midfielder is on Spartak Moscow's books but is already being talked about as one of Europe's biggest talents.
He became the youngest player to score in the Russian Premier League when netting against Lokomotiv Moscow last week at the age of 17 years 8 days.
But Arsenal boss Wenger knew about Ananidze long before he burst on to the scene with that goal as his scouts have trailed him for the past year.
The Gunners face competition from Juventus, AC Milan and Seville for the teenager but fighting off those challengers will be easy compared to persuading Spartak to sell.
Yet another overseas youngster arriving at the Emirates could mean more criticism for Wenger but the Gunners boss is unconcerned.
He said: "In a football team you can have 80 per cent foreigners.
"If that happened in normal society, English people would be upset.
"You have to be prepared to accept the rules of a new country.
"When I was in Japan I ate sushi. And when I am in England I eat roast beef and Yorkshire pudding."
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