The 24-year-old, whose contract runs out in June, will be able to join the Premier League club as a free agent.
The Reds tried to tempt the centre-back to move in this window during their defensive crisis at the start of January, however the Bundesliga side were unwilling to let him leave, while Matip wanted to honour the remaining months of his deal.
Reports in Germany suggesting Liverpool have bid £6m to recruit the Cameroon international ahead of the 11pm deadline on Monday, 1 February are wide of the mark.
Matip, who can also operate as a defensive midfielder, will not line up for the Merseysiders before the summer.
Less than two weeks ago, Klopp explained: “There’s nothing to say about this, to be honest. I don’t know who spoke about it and said something is fixed.
READ MORE | COMMENT: Why Liverpool need Teixeira
“When something is fixed or whatever, you’ll be the first I speak about it with, so there’s nothing else on this.”
Meanwhile, it is understood that Granit Xhaka from Borussia Monchengladbach is not currently a target for Liverpool.
A meeting between Klopp and the player’s representative Andy Gross is thought to have taken place, but it was not in conjunction with the 23-year-old.