Van Dijk joined Mohamed Salah in signing a two-year renewal at the back end of the 2024/25 season as the Reds closed in on the Premier League title.
The pair were vital in getting Liverpool over the line, but fast forward 12 months and Salah has moved on with his contract settled, and Arne Slot has also exited.
35-year-old Van Dijk will see out his own final year at Anfield - as he aims to break the 400 game mark for the club - but his plans beyond that are unclear at this stage.
MLS side Chicago Fire are rumoured to be planning an offer in 2027 after landing Robert Lewandowski last month.
The US giants knew a deal was impossible this summer, but they had hoped to open preliminary talks during Liverpool's USA preseason tour last month, but Van Dijk was not included due to an extended summer break.
Andoni Iraola had indicated Van Dijk could join up for the final days of the tour, but it was decided against, after his exploits at the 2026 FIFA World Cup.