The Reds have been heavily linked with a move to sign the Netherlands international throughout the summer transfer window.
Liverpool were forced to issue a statement apologising to Southampton for their pursuit of Van Dijk in June.
The Merseyside outfit officially ended their interest in the Dutch centre-half in their embarrassing apology.
However, Liverpool continue to be linked with a successful move to sign Van Dijk.
There is reported to be a confidence in the centre-half’s camp that a summer move will happen despite Southampton’s reluctance to sell.
Former Newcastle United striker Quinn, who is a self-confessed Liverpool supporter, believes Van Dijk’s arrival would be sufficient to transform Klopp’s team into title winners.
“[Sadio] Mane’s back fit, they’ve signed [Mohamed] Salah, they’re playing lovely football where they left off last season,” Quinn told talkSPORT.
“I think they’ll be a title challenger and I think if they get Van Dijk and keep [Philippe] Coutinho, they could even with the league.”
The Reds have signed three players in the summer transfer window so far ahead of the 2017-18 season.
Liverpool brought in AS Roma winger Mohamed Salah in a £39m deal from the Serie A giants earlier this summer.
The Merseyside outfit have also added Chelsea teenager Dominic Solanke and Hull City defender Andy Robertson.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news