According to Gazzetta dello Sport, signing the Dutchman is the dream of AC Milan advisor Zlatan Ibrahimovic. The Swede has been pushing for a potential transfer since the spring, according to the report.
Ibrahimovic serves as a senior advisor to Milan's ownership and senior management, a role he took on after retiring as a player and returning to the club he represented across three separate spells during his career.
Milan's majority owner RedBird is now said to be examining the move and assessing whether a transfer would be feasible this summer, given Van Dijk's age and standing in the game.
It is not clear whether the 34-year-old wants to leave Liverpool, or whether the Reds would be willing to let go of the centre-back, who has won 96 caps for the Netherlands.
Alongside Milan, Turkish club Galatasaray are also said to be interested in Van Dijk.
Van Dijk joined Liverpool from Southampton for a then world-record fee for a defender in January 2018 and has since become one of the club's most influential players, winning the Premier League title in 2019-20 and again in 2024-25 as captain, as well as the Champions League in 2019.
The defender's leadership and consistency have made him a mainstay of Liverpool's backline for close to a decade, and any departure would represent a significant change to the club's defensive options under Arne Slot.
Galatasaray's interest adds a further layer of competition to any potential move, with the Turkish champions also understood to be assessing a possible approach.
For now, no formal contact between the clubs has been reported, and Van Dijk's stance on a possible exit from Liverpool remains unknown at this stage.
The Dutchman's contract situation and Liverpool's willingness to sanction a sale this summer are both likely to be significant factors in whether Ibrahimovic's dream move for Milan can become reality.