The Daily Mail says there will also be a need to address the position of Zelkjo Buvac, Klopp's long-term assistant who walked out on Liverpool 26 days before the Champions League final. He remains employed by the club but it is difficult to see how he returns to his old role.
Pepjin Ljinders, who was part of the backroom staff as recently as January, could return to assist Klopp, having left his position as manager of NEC Nijmegen.
Liverpool could add to their medical department at Qatar's sports medicine hospital, Aspetar. Philipp Jacobsen worked with Adam Lallana when the England midfielder visited the clinic last October after rupturing his thigh.