The German midfielder has been heavily linked with a move to the Serie A champions.
Can is out of contract with Liverpool at the end of the season and would be a free agent.
But Reds supporters will be encouraged by their manager's latest update on the saga.
According to CalcioMercato Klopp dismissed suggestions that Can had agreed a new deal with Juventus.
"No. He didn’t come in my office and say so. Nothing new about that," he said.
"I think everything is possible, but there’s nothing else to say about it.
Liverpool’s likely line-up to face Southampton away
Liverpool FC
“I think everything is possible, but there’s nothing else to say about it”
Jurgen Klopp
"There’s no decision made, otherwise we would have said."
Naby Keita is set to join Liverpool from RB Leipzig in the summer.
Can may yet be persuaded to stay at Anfield depending upon what wage packet they can offer the German star.
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Liverpool have not won silverware since a League Cup victory over Cardiff six years ago.
Trophies are virtually guaranteed at Juve. The Bianconeri have landed the Serie A title in their last six consecutive campaigns.
The Kop are back in action at St Mary's later today against Southampton (4.30pm).