Wilshere, 16, will be called into the England Under 19 squad for a friendly against Spain as part of his fast-track towards the national team.
He is already a regular member of the England Under 16s, but a good performance against Spain next February will bring him into consideration for the Under 21 Championship next summer.
Wenger said: "Wilshere will kick on because he is not fazed by anything. He is not fazed by the duels and he relishes the fight. Carlos Vela will also play against Burnley. I played him against Dynamo Kiev because he is doing well and he will play in big, important games."