Sane was omitted from Joachim Low's squad for the World Cup but returned to the fold for the Nations League match against Russia 2018's triumphant team Les Bleus.
However, the 22-year-old's on-pitch body language was questioned by Toni Kroos and he left the squad ahead of the friendly against Peru on Sunday, later confirming it was due to the birth of his daughter.
Werner believes Sane has the attributes to become a key player for Germany, likening him to France star Mbappe.
"I've known him for a long time and played with him in the Under-19s and he always gave everything in games," Werner told Bild am Sonntag.
"Like Mbappe, he can be a huge weapon with his speed and agility."
The RB Leipzig striker went further in his effusive praise of Paris Saint-Germain star Mbappe, claiming he will be the sport's leading star when Lionel Messi and Cristiano Ronaldo hang up their boots.
Werner said: "He's just impressive, even though he's two or three years younger than me. And I'm very young.
"If at some point Messi and Ronaldo should leave, he is certainly one of those who will fill this gap. His potential is breath-taking.
"His speed and ball control are incredible. You have to envy everyone who has him on their team."