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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.