The 19-year-old still has four years left on his current contract with the Gunners.
But The Sun reports that Arsenal are ready to start talks over a new deal for the youngster later this month.
Wenger has seen the likes of Robin van Persie, Cesc Fabregas and Samir Nasri leave the club in recent seasons and is desperate to keep his best players on long-term deals.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?