The Southampton defender was one of Jurgen Klopp's top transfer targets this summer.
But interest in the Netherlands international cooled after Liverpool were accused of trying to illegally approach him.
The Reds' pursuit of him ended in embarrassment with the club being forced to publicly apologise to Saints.
Jurgen Klopp was coy about the Reds reportedly renewing their interest in Van Dijk after his side's 4-0 pre-season win over Tranmere Rovers.
He said: "It would be very wrong to talk about this.”
However, Murphy is confident the defender will end up at Anfield before the transfer window closes.
"Personally, the problem for Liverpool was more defensive (last season),” he told sport.360.com.
“I think the van Dijk thing is close. That would be a phenomenal signing.
“But there's definitely more business to be done at Anfield.”
Liverpool has already been making waves in the transfer window with Mohamed Salah signing in a club-record deal.
Dominic Solanke also joined the Reds on a free transfer from rivals Chelsea.
Klopp is also tracking RB Leipzig midfielder and Arsenal's Alex Oxlade-Chamberlain.
Source: Daily Express