Liverpool are reportedly considering a move to sign Schalke 04 left-back Sead Kolasinac on a free transfer next summer.
Milner has performed excellently since his transition from midfield to defence, while Alberto Moreno has served as a capable deputy when Milner has been unavailable.
However, Milner turns 31 in January, and according to German publication Bild, Klopp has his sights set on a new long-term option for the role.
This comes in the form of Bosnia & Herzegovina international Kolasinac, whose contract with Schalke expires at the end of the 2016/17 campaign.
The Reds would reportedly face competition from West Ham United and Chelsea for his signature, with Kolasinac looking for clarity in his position under manager Markus Weinzierl before he decides on his future.
Kolasinac has played a rotational role so far this season, with Weinzierl calling upon both him and Chelsea loanee Baba Rahman, affording him four Bundesliga starts to date.
This is a departure from the stability he found in previous seasons, starting 18 of his 23 league appearances in 2015/16, after recovering from a crippling ACL injury.
Kolasinac’s spell on the sidelines in 2014 and 2015 could be a cause for concern for Klopp, but the 23-year-old has shown no signs of depreciation since his return to action.
An aggressive, front-footed left-back, Kolasinac would seemingly slot into Klopp’s Liverpool squad comfortably, providing energy on the left of defence.
His recent performance in Schalke’s 0-0 Revier derby draw with Borussia Dortmund served as a showcase of his defensive talents, making three successful tackles, three interceptions and six clearances, thwarting another Liverpool target, Christian Pulisic, with a goal-line block.
He is also able moving into attack, though he has scored just one goal and laid on eight assists in his 95 appearances for Schalke so far.
One of the key positives for Klopp is that discussions can begin with Kolasinac as early as January, as was the case with another Bosman signing from his former rivals, Joel Matip.
Matip left Schalke for Merseyside after seven years in the first team at the Veltins-Arena, with his move announced on February 15.
The Cameroonian’s excellent start to life in the Liverpool defence should encourage Klopp to dip into the free-transfer market again, with Matip’s former team-mate an excellent addition.