The right-back has been sidelined since pre-season with a back problem that is expected to keep him out of action until at least November.
Bradley featured for the Reds in the summer friendlies against Karlsruher and Furth in Germany but was left out of the squad that subsequently travelled to Singapore.
He returned from a loan spell with Bolton last season to act as cover for Trent Alexander-Arnold but has yet to feature competitively for Liverpool since coming back from the League One side.
Speaking ahead of the trip to Brighton, Klopp revealed that the 20-year-old is “on the way back” with his recovery and is running at the training ground, but he also explained why the process cannot be rushed.
“Conor is on the way back with running, but in that age group and with these kinds of injuries you tend to give them three weeks more than not enough because it has to do with the growing process of the body, stuff like this,” the boss told the media.
“I couldn’t get this injury any more, let me say it like that, and that’s why they need a bit of time.”
The fact that Bradley is running at Kirkby is a positive development given the unfortunate nature of the issues he has suffered so far this season.
It was revealed in August that the injury was a long-term one, with Northern Ireland manager Michael O’Neill claiming that the youngster was an “extreme doubt” for the international friendlies that are set to end on November 20.
Klopp has been more tentative in providing a timeline for Bradley’s return, but he will be keen to see him back on the pitch sooner rather than later.
Liverpool’s first-choice right-back Alexander-Arnold has himself dealt with fitness issues this season having only returned from a hamstring injury last weekend against Tottenham.
Bradley has five senior appearances for the Reds to his name and will be hoping to add to that tally this season when he gets back to full fitness.