James Milner will begin full training with the Liverpool squad when they return from their pre-season trip to Germany.
The midfielder has been struggling with a quad injury since their Premier League Asia Trophy clash with Leicester City on Saturday.
"It was clear from the first day there's a little bit of tendon involved, so that means that it's around 10 days," Klopp told the club's official website.
"That means he will do his rehab here in Germany and then should be fit again when we're at home.
"With injuries, you can't be sure but it shouldn't be much longer."
Hello from the Olympiastadion Berlin. July 27, 2017
While there is good news on Milner, Klopp remains unsure when Nathaniel Clyne will return from his back problem.
"This is maybe the longest Clyney has been out with a little bit of [an issue with] the back," the Liverpool boss added.
"We have to wait, time is running and we need Clyney of course."
