The Reds have been linked with the Netherlands international throughout the summer transfer window so far.
Liverpool were forced to apologise to Southampton for their pursuit of the 26-year-old defender in June.
The Merseyside outfit issued a statement officially pulling out of the race to sign the former Celtic defender.
Van Dijk, though, is still being tipped with a switch to the 20-time English champions in the summer transfer window.
The 26-year-old has been training away from the rest of his Southampton team-mates in pre-season ahead of the 2017-18 season.
Liverpool have already signed AS Roma winger Mohamed Salah, Chelsea teenager Dominic Solanke and Hull City defender Andy Robertson.
While Thompson backed Liverpool’s signing of England Under-20 international Solanke, the former Reds captain is confident Van Dijk will also complete a switch to Anfield.
“I think the Van Diijk deal will still happen and I think Dominic Solanke was a fantastic steal from Chelsea,” Thompson told Sky Sports.
“I hope he gets the game time he’s joined for.”
Liverpool finished in fourth place in the Premier League table to secure a return to the Champions League after a two-season absence.
The Reds are still waiting to win their first piece of silverware under Jurgen Klopp after the former Borussia Dortmund coach was appointed as Brendan Rodgers’ successor in October 2015.
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