The Senegal international has been out of action since damaging his knee against Everton on April 1, ruling him out of the Reds' final eight games of last season.
It was revealed last week that the 25-year-old's return would not come before Liverpool's trip to Hong Kong, where they are competing in the Premier League Asia Trophy.
Mane will link up with his teammates at their Melwood training ground next week, before jetting off to Germany for the next stage of the Merseyside outfit's preparations for the new campaign.
"Sadio is on the way back. The plan is he will come with us to Germany," Klopp told the club's official website. "The plan is he trains completely normally with us when we are back in England.
"We have been waiting long enough for him now! He is around [Melwood] all of the time and is in pretty good shape. Unfortunately he was not ready to train, but he looked good, it looks good and so now he should be fine when we get back."
Liverpool take on Hertha Berlin and Bayern Munich during their time in Germany, as well as one of Napoli or Atletico Madrid as part of the 2017 Audi Cup.