The position at Anfield has been vacant for a few weeks now, as Jorg Schmadtke - who was only hired last year - departed the club upon the expiration of the January transfer window.
Schmadtke stepped into the void left by Julian Ward, who served as Liverpool's sporting director for just one season before resigning from his post, allegedly due to family reasons.
Prior to Ward's appointment, Michael Edwards was the Reds' long-serving transfer guru, overseeing the captures of numerous big-money signings who have now cemented their place in Liverpool folklore.
However, the Reds are set to head into the post-season period without a sporting director as things stand, but the club supposedly want to hire a new chief before ramping up their search for a successor to departing head coach Jurgen Klopp.
According to Football Insider, Bayer Leverkusen's Simon Rolfes is one name on Liverpool's shortlist, and the Reds are already targeting his colleague - Xabi Alonso - to become their new first-team manager.
Rolfes retired as a player at Leverkusen in 2015 and has since gone on to serve as their academy manager, sporting director and managing director of sport, masterminding the acquisitions of several key performers.
The likes of Edmond Tapsoba, Granit Xhaka, Patrik Schick, Odilon Kossounou, Alejandro Grimaldo, Victor Boniface, Jeremie Frimpong, Piero Hincapie and Robert Andrich - most of whom have played integral roles in Leverkusen's Bundesliga title charge this term - have all been signed with Rolfes at the helm.
However, Leverkusen recently tied Rolfes down to a new long-term contract until the summer of 2028, meaning that Die Werkself would be in line for a hefty compensation package if he were to depart this summer.
As well as the 42-year-old, a separate report from The Athletic claims that Liverpool have also been running the rule over Frederic Massara, who was sporting director of AC Milan until his departure last summer.
Following a brief career as an assistant manager with Benevento, Palermo and Pescara, Massara moved into football administration with Roma, taking on secretary and sporting director roles before joining Milan in 2019.
The Rossoneri won the 2021-22 Serie A title with Massara in office, but he was placed on gardening leave by the Rossoneri last year, meaning that he would be able to take up the Liverpool job immediately.
Finally, Nice chief Florent Ghisolfi is also said to be under consideration thanks to his work with Les Aiglons and Lens, whom he helped transform from a Ligue 2 side into Ligue 1 title challengers during his stint at the Stade Bollaert-Delelis from 2019 to 2022.
The 38-year-old only joined Nice in October 2022, several months before overseeing the appointment of new boss Francesco Farioli, who has Les Aiglons third in the Ligue 1 table after 22 matches.
However, the report adds that Nice's owners INEOS - who now own a stake in Manchester United - will fight tooth and nail to retain Ghisolfi's services if Liverpool come knocking this summer.