The 22-year-old departed PEC Zwolle in the Netherlands to join up with Klopp's team in the summer of 2019, but he has only racked up a paltry four appearances for the Reds' senior squad.
All four of those matches came during Van den Berg's debut campaign, where the Dutchman made three appearances in the EFL Cup and also started an FA Cup fourth-round replay win versus Shrewsbury Town.
Van den Berg has not made another senior appearance for the Reds since the first COVID-19 lockdown, and the closest he has come to a Premier League debut is four successive games as an unused substitute at the start of the 2022-23 campaign.
The Dutchman is currently in his third loan spell away from the club, previously turning out for Preston North End and Schalke 04 before returning to Germany with Mainz 05, with whom he boasts two goals in 23 matches.
Owing to his strong form in the Bundesliga, Mainz may choose to pursue a permanent move for Van den Berg in the summer, but there is no option or obligation to buy the defender in the terms of his loan deal.
As a result, Van den Berg is due to return to Merseyside at the end of the campaign and is under contract at Anfield until 2026, but several centre-backs are already ahead of him in Klopp's pecking order.
The Netherlands Under-21 international is therefore under no illusions that his time with Liverpool could soon come to an end, telling Voetbal Nieuws: "If I go back to Liverpool, they might want me to stay. If I see that I won't get much game time, then I might choose to leave. It's really important to me that I play."
Virgil van Dijk and Ibrahima Konate are Klopp's undisputed first-choice pairing when fully fit, and the duo will be expected to continue their effective partnership once the German passes the reins over to a successor this summer.
Joel Matip is due to leave when his contract expires at the end of the season, but an extension has not been ruled out for the Cameroonian, and academy product Jarell Quansah has also become an important player for the Reds this term.
While Van den Berg believes that he is capable of handling the pressure to play for Liverpool, he accepts that earning starts over Konate and Van Dijk could be too big an ask, adding: "In previous years, I didn't feel like I would be starting next to Virgil. I don't know yet what my chances will be like next summer.
"I think I'm doing well. I can handle playing at Liverpool. I can compete. But being a starter is different. Virgil and Konate are not easy to beat. I know it will be hard."
As well as Van den Berg, Liverpool may sever ties with two other forgotten centre-backs in Nat Phillips and Rhys Williams, who were recalled from previous loans in January and sent out to Cardiff City and Port Vale for the remainder of the 2023-24 season.
However, Williams's time with Port Vale was cut short almost immediately as an underlying injury was uncovered, leading to the Englishman returning to Liverpool to undergo treatment.