The forward was absent from Liverpool's team against Nottingham Forest in light of the incident.
Klopp told reporters that the Colombian international wanted to go home but he did not say if he would.
The Colombia Football Federation has appealed to the kidnappers to release the father of the 43-time international.
"We ask the captors of Luis Manuel Diaz, father of Luis Fernando Diaz, to release him now, without conditions," the Colombian FA posted on X, formerly known as Twitter.
The Colombian police have announced a reward of 200 million Colombian pesos ($48,300) for information leading to the rescue of Diaz's father.
Persons:
Diogo Jota, Liverpool's Luis Diaz, Scott Heppell, Luis Diaz, Juergen Klopp, Diaz's, Cilenis Marulanda, Gustavo Petro, Klopp, Diaz, Luis Manuel Diaz, Luis Fernando Diaz, Chiranjit, Robert Birsel
Organizations:
Soccer Football, Premier League, Liverpool, Nottingham Forest, REUTERS, Authorities, Colombian, Colombia Football Federation, Colombian FA, Thomson
Locations:
Anfield, Liverpool, Britain, Colombia, Bengaluru