The Dutchman, 26, looked to be nearing a move to Anfield in August before the Saints blocked his move.
Souness, who had spells managing both Southampton and Liverpool, is now hoping the Reds can strike a deal in the new year after failing with a £60million bid this summer.
And Liverpool desperately need him.
After just six Premier League games the Reds have coughed up 11 goals – the joint-third worst record in the division.
Souness reckons Van Dijk would help solve the problem.
The Scot said: “I am a fan of Van Dijk. When he was at Celtic I thought it was too easy for him. He makes it look simple.
“Anybody who makes the job look easy is worth keeping an eye on.
“He looks like he can outpace anyone and out-jump anyone. He is always comfortable on the ball and whenever someone is like that, it is the mark of class.
“I’d love him to go to Liverpool. He is the stand-out centre-half at his football club.
“The question when you play for Saints or Blackburn or Bolton is can make that jump to the big stage?
“You don’t know until they walk through the door.
“But he has played in front of 60,000 fans at Celtic so he has been in front of big crowds.”
And Souness is not the only Koppite saying Van Dijk is the answer.
Ronnie Whelan believes the Holland international can answer Liverpool’s defensive prayers.
And he has told Liverpool boss Klopp to stop being so attacking.
Whelan said: “Defensively they haven’t got the level of players the other teams have.
“You have to worry about the manager and ask does he not see what’s going on?
“Liverpool defensively aren’t good enough to go with this all-out attack.”
Graeme Souness was speaking at the launch of TV3’s Champions League coverage.
