Reus suffered a ligament tear in Germany's World Cup warm-up match against Armenia in June, ruling him out of the tournament, and sporting director Michael Zorc has said this week that the player is still expected to return to action in September.
Klopp feels that Reus could make a return to team training in a matter of weeks after his ankle has shown positive signs of progress.
Speaking to Bild, Klopp said: "It's always a good feeling to see the guys running again. This is great. So far, the healing process has been optimal.
"Maybe Marco can get into the team training again in two or three weeks."
Reus scored 23 goals for Dortmund last season, helping BVB to a second-placed Bundesliga finish behind Bayern Munich.
However, Klopp added that there would be no rush for the forward to return to action.
"We will not put Marco under pressure. We will give him all the time he needs," he said.