Luis Diaz returned to Liverpool's squad as a substitute for Sunday's Premier League match at Luton following his parents' kidnapping in Colombia.
Diaz, 26, had not featured in the Reds squad since their Europa League win over Toulouse on 26 October.
Luis Manuel Diaz and his wife were seized at gunpoint on October 28. Diaz's mother was found in Barrancas but his father remains missing.
"Negotiations are ongoing, but it is positive," said manager Jurgen Klopp.
"All the signs he gets as I understand it are very positive. That is why he wanted to be part of the team and he could come on as well.
"From that point of view I have no issue, but nobody can imagine how something like that feels. On the training ground he has been fine and that is why he is here."
Diaz resumed training at Liverpool on Wednesday. He was absent from the Liverpool side that beat Nottingham Forest 3-0 on October 29, during which team-mate Diogo Jota held up Diaz's number seven shirt after scoring his side's first goal.
The Colombia international was also absent for the EFL Cup last-16 win against Bournemouth on Wednesday.
The Colombian government said Diaz's father was kidnapped by left-wing rebels of the National Liberation Army (ELN), sparking a major military and police search.
A representative of the group has reportedly said it will free Diaz's father in the coming days.
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