The 18-year-old enjoyed a breakthrough campaign for the Reds across 2022-23, making 19 appearances in total and scoring his first senior goal for the club at Aston Villa in December.
Bajcetic's involvement ended prematurely in March due to injury, however, and he has since been undergoing rehabilitation.
Asked for the latest on his condition, Klopp told journalists during the second part of Friday's press conference: "Yeah, there's progress. I spoke yesterday [with him] along with the doc. There will be - around [the] start of pre-season - there will be parts of reintegration, but that will take time.
"So, he's not in full training. That's the prediction at the moment. He's completely pain-free, but we talk about a very young player and a very young body, so we have to be careful.
"It's a different injury, obviously, but we had to be super-careful with Curtis [Jones]. It's annoying for the player, really annoying, because you can train two days and then you need two days off, but you feel great, but it's just [so you] don't take any risk.
"That might be a little bit the plan for him, [but] when that exactly starts, I don't know. I hope that he can come with us in the training camp and can do these bits and from then on progress. Then he should be fine for the start of the season, but it's how it is with these kind of injuries.
"There's no real timeline that you say after six weeks, or whatever, the ligament is healed and now from there we can go. We don't know that. You have to wait always for the next assessment and if you know that then you can go from there.
"But it's positive, I think at the end of the pre-season he will be hopefully a week or two already in full training and before that parts of training. So, that should be fine."