The Revolutionary Armed Forces of Colombia said they may no longer release the general due to military actions in the Choco region where General Ruben Alzate was taken.
Troop deployments, aircraft overflights and movement-restricting security measures have brought life in the jungle region to a standstill.
"These communities have been practically besieged by the army," the FARC said in statement from its delegation in Havana.
As long as the military maintains a heavy presence in the jungle, Alzate and other soldiers are unlikely to be freed, the guerrilla group said.
The FARC also holds two soldiers captured near the Venezuela border.
Alzate was kidnapped November 16 in the remote Choco region, sending into disarray peace talks aimed at ending Latin America's longest-running insurgency.
The 50-year struggle has claimed more than 220,000 lives, AFP reported.
Colombian President Juan Manuel Santos suspended the two-year peace negotiations after the kidnapping.