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.
‘Newcastle’s board said I was over the hill, so I left and played 108 consecutive games and won the European Cup – not a bad way to answer that accusation!’: Ex-Magpies defender reflects on career highlight after proving former side wrong
‘Parma viewed him as the perfect replacement for Adrian Mutu, who’d left to sign for Chelsea. But Manchester United’s interest was much more concrete’: Cristiano Ronaldo's 2003 transfer details revealed by former Sporting director of football
