Reus suffered a partial tear of the ligament in his left ankle in Germany's World Cup warm-up match against Armenia last month.
The injury forced Reus to miss Germany's successful campaign in Brazil as Joachim Low's men claimed their fourth world title.
Dortmund forward Reus had been expected to be unavailable for three months.
However, Klopp has now suggested that the 25-year-old's comeback may be much earlier than anticipated.
"It's always a good feeling to see the guys running again. This is great. So far, the healing process has been optimal," Klopp told Bild.
"Maybe Marco can get into the team training again in two or three weeks."
Reus enjoyed a fine 2013-14 campaign with Dortmund, scoring 23 goals in all competitions.
But, despite his importance to the team, Klopp was quick to stress that he will not hurry the former Borussia Monchengladbach man back.
"We will not put Marco under pressure," he added. "We will give him all the time he needs."