The Holland international has established a reputation as one of the Premier League's best centre-backs since joining Saints from Celtic in 2015.
And in January the first rumours about a potential switch to one of the top flight's big boys started to emerge.
Liverpool, Chelsea and Manchester City were all credited with strong interest in getting Van Dijk on-board.
And an Anfield switch appeared to be a formality until the Reds were accused of tapping the 26-year-old defender up in June.
That situation meant Liverpool were forced to officially pull out of the race to sign Van Dijk.
And Jurgen Klopp opted not to target any other players instead.
Last week Van Dijk revealed his interest in quitting Southampton when the transfer window reopens.
And the Daily Mail indicate Liverpool would still be in the queue of clubs keen to snare him.
The newspaper say Van Dijk remains a "prime objective" for Liverpool.
Whether Southampton will consider offers for the former Groningen man in January remains to be seen though.
Liverpool, meanwhile, return to Premier League action against Manchester United on Saturday.
Klopp's side are currently seventh, having collected 12 points from their opening seven games.
Van Dijk could play for Saints on Sunday when they host Newcastle at St Mary's (4pm).
