Liverpool are expected to sign Ben Davies from Championship side Preston to ease their defensive crisis before a quiet January transfer window closes late on Monday.
The Premier League's leading clubs have been unusually restrained this month, with the coronavirus and new Brexit rules dampening the market after a big summer spend.
The January window, which closes at 2300 GMT, is typically regarded as a seller's market and often a time for stopgap measures but Liverpool have been forced to act.
The champions are missing all of their senior central defenders, with Virgil van Dijk, Joe Gomez and Joel Matip out of action. First-choice back-up Fabinho recently joined the injured list.
It us understood that Liverpool have agreed a fee with Preston for the 25-year-old Davies.
A medical was scheduled for Monday, with 19-year-old Dutchman Sepp van den Berg likely to head the other way on loan for the rest of the season.
Liverpool are also reportedly interested in Marseille centre-back Duje Caleta-Car but the Ligue 1 side's struggle to find a replacement at short notice could scupper any potential move.
Klopp, whose side are third in the Premier League table, admitted on Friday that no club would be prepared to sell him an "£80 million ($110 million) centre-back" in the final days of the transfer window.
"This calibre of player the teams would not sell them now," he said. "We need to find the right player and one which suits our financial situation, that's clear as well."
- Alli to PSG? -
Uncertainty lingers over the future of Tottenham midfielder Dele Alli, who has been linked with a loan move to Paris Saint-Germain, now managed his former boss Mauricio Pochettino.
The England midfielder has been out of favour at Tottenham under Jose Mourinho, barely featuring in the Premier League this season.
Mourinho said last week he was not expecting Alli to depart but admitted "sometimes unexpected things can happen".
Major moves involving "Big Six" Premier League clubs appear unlikely on Monday.
Among the few eye-catching deals that have taken place over the past month, Manchester United midfielder Jesse Lingard has joined West Ham on loan after slipping down the pecking order at Old Trafford.
Real Madrid midfielder Martin Odegaard has arrived at Arsenal, also on a loan deal, while Mesut Ozil made a much-anticipated exit from the club, joining Turkish giants Fenerbahce.
Aston Villa last week signed French midfielder Morgan Sanson from Marseille in a deal worth a reported £15.5 million.
Struggling West Brom have made three signings, including the loan capture of Galatasaray striker Mbaye Diagne.
And boss Sam Allardyce was quoted after Saturday's 2-2 draw with fellow strugglers Fulham as expressing his desire to add to that before Monday's deadline.
Tim Bridge of Deloitte's Sports Business Group told the Press Association news agency that clubs were being cautious because of their straitened circumstances.
"I think this month more than ever feels as if clubs are taking a bit of a watching brief and are not currently willing to spend in the way they previously have done," he said.
"That's a reflection of the fact that all clubs have suffered a huge revenue loss, everybody's aware of that, and I think clubs are slowly trying to understand what that means for their business models.
"So I think naturally there's probably an element of consideration, of taking the time to understand exactly where the market's at, and I would imagine people making the decisions at clubs at the minute are probably struggling to understand what represents true value."