Van Dijk is set for a lengthy spell on the sidelines after learning that he will need surgery on the knee injury he picked up against Everton on Saturday.
Liverpool decided against moving for a new central defender during the summer but were heavily linked with Brighton's Ben White after he starred on loan at Championship winners Leeds United last season.
Football Insider reports that the 23-year-old is still on the Reds' radar, and that they could accelerate their plans to sign him by making a move in January given Van Dijk's absence.
However, the report also claims that Liverpool have reservations over White's aerial presence after scouting him intensively.
Brighton are thought to value White at more than £30m after rejecting a number of bids from Leeds during the summer transfer window.
The defender has featured in every game for Graham Potter's side so far this season, although the Seagulls have shipped 14 goals in six matches across all competitions in 2020-21. body check tags ::