The French under-18 international has also been attracting the interest of Italian giants AC Milan since starring in the European under-17 Championships last summer.
Gouiri who is under contract until 2020 trains with the senior Lyon side and is tipped to make his senior debut before the end of the season.
The Gunners signed Alexandre Lacazette from Lyon in the summer and have been regular visitors to Lyon youth matches watching Gouiri in action.
Gouiri is rated as one of the most exciting talents in French football and Lyon could decide to cash in on him and let another club develop him.
Wenger has always had a keen eye on the French market and it could give him an advantage when it comes to signing Gouiri.
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