Diaz's father was released last week after being held for 12 days by the ELN guerilla group.
Luis Manuel Diaz was seized along with his wife Cilenis Marulanda on October 28th.
Marulanda was rescued hours later and a massive search operation by ground and air was launched for her husband.
Luis Diaz was reunited with his parents on his return to Colombia for international duty on Tuesday.
The Liverpool forward then went on to score both goals in a fairytale 2-1 win over Brazil in World Cup qualifying.
Liverpool chartered a private flight that arrived in England on Saturday for Diaz's parents and wider family members to spend the festive season on Merseyside.
Diaz will join them in England after representing Colombia in Tuesday's World Cup qualifier away to Paraguay.
The Reds have a hectic fixture schedule on their return from the international break with 11 matches between November 25th and January 1st.