The Reds were rocked by Julian Ward's decision to step down from his post at the end of the 2022-23 season, which came only months after he succeeded Michael Edwards.
In response, Liverpool brought Jorg Schmadtke to the club after his five-year spell with Wolfsburg came to an end, and the 59-year-old oversaw the Reds' summer midfield reshuffle.
Rather than place all their eggs in one basket with Jude Bellingham, Liverpool walked away from a bank-breaking deal for the Englishman to undergo a complete rebuild with the signings of Ryan Gravenberch, Wataru Endo, Dominik Szoboszlai and Alexis Mac Allister.
Liverpool's refreshed engine room has been key to the Reds' solid start to the 2023-24 campaign, which has left them fourth in the Premier League table with 17 points from their opening eight games.
However, Schmadtke is only contracted to Liverpool until the end of the season, and according to Bild, the Reds have identified another Germany-based chief in Eberl as his potential successor.
After retiring as a player in 2005, Eberl took charge of the Borussia Monchengladbach academy for three years, before transitioning into the role of sporting director at the start of the 2008-09 season after Monchengladbach's promotion to the top flight.
The former Germany youth international remained in office for 14 years, during which time Monchengladbach achieved four top-four finishes, most recently breaking into the Champions League places in the 2019-20 season.
Eberl also nurtured talents such as Granit Xhaka, Marco Reus, Marc-Andre ter Stegen and Thorgan Hazard, as well as bringing Marcus Thuram, Yann Sommer and Denis Zakaria to the club.
The 50-year-old ended his lengthy association with Monchengladbach to join RB Leipzig in December 2022 as their Managing Director of Sport, but he left his post after only nine months.
The report alleges that Eberl was sacked as Leipzig felt that he lacked loyalty to the club, having flirted with the idea of joining Bayern Munich, who will be Liverpool's biggest threat to his signature.
Reds' CEO Billy Hogan has apparently already been in contact with Eberl, who had a "non-binding conversation" with the Liverpool chief during last year's Champions League group-stage game between Jurgen Klopp's side and Rangers.