The defender completed a temporary switch to the Championship side last July after signing a new long-term contract with the Reds.
However, injury meant the 23-year-old was unable to make a competitive appearance for Derby, and he will now conduct his rehabilitation at the AXA Training Centre.
Beck, a product of Liverpool's Academy set-up, has appeared three times for the club's senior team to date, having debuted in October 2021.
