The Liverpool Echo says Kent will be assessed by Klopp during pre-season before a decision is taken on loaning him out.
The 20-year-old winger enhanced his reputation with a successful stint at Barnsley last term - chalking up 45 appearances en route to being crowned the Tykes' Young Player of the Year.
However, the Reds are in no rush to decide his next move. Kent will return to Melwood early next month for Klopp to assess his development. He could feature in the friendlies against Tranmere and Wigan prior to the Far East tour.