The 23-year-old has little over six months left on his current contract and with little sign of a resolution imminent, could become the latest high-profile star to flee Emirates Stadium.
But his manager is adamant the former Southampton starlet maintains a deep affection for the club he joined as a 16 year old back in 2006 and is seeking a swift and amicable resolution.
Wenger told reporters: "He belongs here. I want it resolved with the same intensity. I think he loves the club and the club loves him."
The England international's treble against the Magpies was kick-started by a superb goal that saw him cut in from the left flank and curl an unstoppable shot past Tim Krul, reminiscent of several strikes scored by Gunners legend Thierry Henry - which the Frenchman also picked up on.
Wenger beamed: "That was a Thierry Henry-type goal.
"He has done very well, it typifies what I think he can do. He can play through the middle, he will only get stronger.
"He is a good finisher, he has learned a lot because he is an intelligent player. He will continue to improve."