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Lijnders revealed that he made an impassioned plea to his boss to consider keeping Bradley, but Klopp insisted that the youngster would benefit more from a loan spell where he is playing regularly than joining up with Liverpool's squad.
And Lijnders, who was recently dismissed as head coach of Red Bull Salzburg, recalled how the disagreement over Bradley sparked a heated discussion with Klopp.
And with doubts circulating over Alexander-Arnold's future at the club, Bradley, 21, will be primed to take his role at right-back should the England star leave for Real Madrid on a free transfer, with his contract due to expire in June.
It wasn't the first time that Lijnders and Klopp had shared differing opinions on how the Liverpool squad should be managed.
The Dutchman previously said he pleaded with Klopp to trial Alexander-Arnold in a hybrid midfield role due to his influence in their attacking play and even vowed to give him "all my f***ing salary" to make it happen.
He told Redmen TV that he would be "done" if the switch wasn't put in place, explaining: "My idea constantly was: the best No.
What I said constantly to Jurgen was: 'We have to do it.'
'But Pep, blah blah blah" [Klopp complained].
I can't'."
Eventually, Alexander-Arnold took up the dual role as a right-back and stepped into midfield, a role he also took on during his international duty with England.
Lijnders was often hailed as an influential figure behind the scenes and played an important role in helping Klopp find extra margins to challenge in the Premier League and Europe.
After arriving in 2014 as a youth coach, he was bumped up to the senior setup to work alongside Klopp when the German was hired in 2015.
The pair both departed in June after Klopp stepped down from his role as head coach, with Arne Slot given carte blanche to bring in his own team.