The trio are now eligible to play for Liverpool in the knockout stages of the competition, which resumes with a last 16 tie against FC Porto later this month.
While record-signing Van Dijk is still working his way back to full fitness, Clyne is still yet to feature for Liverpool this term after suffering a back injury during pre-season in July.
Klopp says Clyne is making progress but confirmed the England international will not feature against Porto later this month.
"Clyney is not in team training yet but he is in really good way," Klopp said ahead of Liverpool's clash with Tottenham, live on Sky Sports Premier League.
"He is close but after so long out it will take him a while to be ready to play. He has no chance to play in the next round against Porto."
Philippe Coutinho, who made a £146m switch to Barcelona at the beginning of the January transfer window, has been removed from Liverpool's squad list.
Also out of Liverpool's squad are Daniel Sturridge, Marko Grujic and Jon Flanagan who left Anfield in January on loan to West Brom, Cardiff and Bolton respectively.
