The Reds suffered a major defensive crisis last season that derailed their hopes of retaining the Premier League title.
Virgil Van Dijk suffered a serious knee injury in October that saw him miss the rest of the season while Joe Gomez suffered a similar fate the following month.
Joel Matip had his campaign curtailed with an ankle issue in January and Trent Alexander-Arnold was also forced to miss EURO 2020 with a thigh issue.
The four players have been included in Liverpool’s pre-season tour in Austria and Klopp has given an update on their conditions.
"All four look really good, I have to say. Look really good," Klopp said.
"Now we are in constant talks with the medical department, the fitness department, the rehab department about what is right for them today: do they have to do maybe a little bit more than the rest of the group, do they have to do a little bit less?
"So, especially Virg and Joe will not have double sessions now for the first few days with the team; they have a second session of the day but it’s with Andreas Schlumberger, with the rehab department, physiotherapy, these kinds of things. That’s for these two.
"[They] look really good. I don’t know exactly when we can make the next steps but it will happen in the next four weeks, for sure – we will get a big step forward.
"Joel looks good, absolutely, he is the closest probably to normal training and then we will see when we get him started for playing."
“Trent was a serious enough injury but now not a major one, I would say," Klopp added. "He is close but in the moment, probably the next five or six days he has a special programme: from time to time with the team, probably from time to time by himself. But then in five or six or seven days he should be in normal team training.”
