Luis Diaz returned to Liverpool's squad as a substitute for Sunday's Premier League match at Luton following his parents' kidnapping in Colombia.
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.