It is well-documented that the Dutchman is in the final year of his contract with the Reds, meaning that he can sign a pre-contract agreement with foreign clubs in January if no new deal is agreed by then.
At 33 years of age, Van Dijk is not expected to be handed a long-term renewal by Anfield chiefs, although the club are thought to be preparing to sit down with his camp and discuss an extension.
Whether an agreement can be reached is another question entirely, as while Van Dijk recently insisted that he was relaxed about his future, he could be offered a once-in-a-lifetime wage by clubs in Saudi Arabia.
According to CaughtOffside, Liverpool are worried that the Netherlands international could reject a renewal and jump ship for Saudi Arabia next summer, and they have identified a highly-rated Serie A defender as an ideal successor.
Liverpool 'want Juventus' Gleison Bremer' as Van Dijk successor
That man is Juventus and Brazil centre-back Gleison Bremer, who has established a reputation as one of the best defenders in the Italian top flight since joining the Old Lady from Torino for £39.6m in 2022.
The 27-year-old has scored eight goals and set up one more in 86 matches for the Bianconeri across all competitions, and he has helped Thiago Motta's side keep clean sheets in their first three games of the 2024-25 Serie A season.
Bremer - who was also a member of Brazil's 2024 Copa America squad - was thought to have been a prime target for Manchester United in the summer, but he snubbed the Red Devils to sign a new long-term contract with Juventus.
The 6ft 2in centre-back's terms in Turin do not expire until 2029, although there is believed to be a €70m (£59.1m) release clause in his contract, which will activate in the summer of 2025.
It is unclear whether Man United will reignite their interest next year, having captured Leny Yoro and Matthijs de Ligt after conceding defeat in the race for Bremer, whose former Juve teammate Federico Chiesa signed for Liverpool in a bargain £10m deal this summer.
Could Liverpool duo follow Van Dijk to Saudi Arabia?
Van Dijk is one of three cherished Liverpool players out of contract next year - the others being Mohamed Salah and Trent Alexander-Arnold - while Alisson Becker's long-term future is also the subject of much debate.
The report adds that all of Van Dijk, Salah and Alisson are 'looking likely' to leave Anfield for Saudi Arabia in 2025, where the latter's long-term successor Giorgi Mamardashvili will arrive from Valencia.
Despite admitting that he was planning for the 2024-25 season as if it was his last at Liverpool after last weekend's 3-0 win over Manchester United, Salah is apparently keen to stay on for a little while longer, but contract talks with his entourage are yet to begin.
However, Liverpool are optimistic of reaching an agreement to extend the contract of academy graduate Alexander-Arnold, in spite of persistent links with Real Madrid.