The 26-year-old scored the decisive penalty against Argentina last Saturday with a cool 'Panenka' to secure the historic trophy for his country.
The forward enjoyed a stunning debut campaign at Arsenal last season after joining from Barcelona in a £32m, topping the club's scoring charts with 25 goals.
And while he is expected to miss the start of the season as Wenger gives him an extended break, the Frenchman revealed Sanchez is already focused on bringing more silverware to the Emirates.
"I texted him [after the final] and he texted me back," Wenger said.
"He was already focused on next season with Arsenal and wants to win everything with us. He was thrilled and very happy.
"They had quite a comfortable lead when he took the penalty but I was a bit worried because he missed one with us.
"He has shown again that he is scared of nothing. He took the ball and chipped the keeper. It was quite audacious but I was of course over the moon to see him bring the trophy to a country that has waited for such a long time.
"It is an historic achievement and when you're a football player, you want to do that, so I'm very happy for him."
