The rebel group holding Luis Diaz's father hostage has demanded "security guarantees" before his release.
The National Liberation Army (ELN) said the ongoing military and police search "will delay the release and increase the risks", Colombian media reported.
Luis Manuel Diaz was kidnapped at gunpoint along with his wife in Barrancas, Colombia on 28 October.
Liverpool player Diaz has called on the kidnappers to free his father immediately and end a "painful wait".
His mother was abandoned in a car after the kidnapping as police closed in, but his father was taken hostage.