Reus was cruelly ruled out of Germany's successful World Cup campaign after tearing the anterior ligament above his left ankle in a friendly against Armenia in June.
The injury was expected to sideline the 25-year-old until September.
However, Reus is confident he will soon be back in action.
"I can move quite normally and run [in] training," Reus is quoted as saying by Bild.
"It is important for me that I will quickly [be] healthy and can play again soon."
Reus, who did not put a specific timescale on his recovery, has scored 30 goals in 62 Bundesliga appearances for Dortmund since joining from Borussia Monchengladbach two years ago.