The 23-year-old was first tipped to make the move to Anfield during his time with Ajax, having impressed against Jurgen Klopp's side in the 2020-21 Champions League.
However, with Liverpool instead opting to poach Ibrahima Konate from RB Leipzig, Schuurs instead swapped the Netherlands for Serie A, joining Torino last summer.
The Italian top-flight side paid just £8.1m for his services, and Schuurs has continued his upward trajectory in Serie A, scoring one goal and providing two assists in 33 games in his debut season.
The 6ft 3in defender is under contract with Torino for another three years, but links with Liverpool have resurfaced as Klopp seeks to bolster his backline.
Schuurs is believed to have travelled to England in order to watch his sister - a professional tennis player - compete at Wimbledon, while simultaneously holding talks with interested parties.
As well as Liverpool, Crystal Palace and West Ham United are rumoured to be interested in a deal for Schuurs, and the Eagles are already said to have made a lucrative offer.
Without naming names, Schuurs recently confirmed that "offers" had arrived, and both his agents and Torino are "evaluating" the proposals made by the unnamed teams.
"I don't know if I'm staying. I don't know if I'll leave for Pinzolo on Monday, my agents and the club are evaluating the offers that have arrived," the Liverpool Echo quotes Schuurs as saying.
The Dutchman's contract with Torino also includes an option to extend until 2027, and the Italian side are believed to be open to bids of around £34m this summer, but no team is said to have reached their valuation yet.
Liverpool's summer recruitment drive has previously been focused on midfield additions, and Klopp has welcomed both Alexis Mac Allister and Dominik Szoboszlai to Anfield so far this summer.
The Reds are thought to be open to adding another new lynchpin to their ranks ahead of the 2023-24 season, but a centre-back could also arrive in anticipation of a couple of defensive departures.
Rhys Williams and Calvin Ramsay have both left on loan for Aberdeen and Preston North End respectively, while Nat Phillips is also expected to depart and is said to be on Feyenoord and Leeds United's radar.
Joel Matip - who fell down the pecking order last term - is another centre-back facing an uncertain future, as his deal with the Reds only runs until the end of the 2023-24 season.