Talley's fishing vessel, Janas, was also heading to the area and was expected to take three to four days to reach the edge of the ice.
US Coast Guard Vice Admiral Charles Ray, commander of Pacific Area, said the seas of Antarctica were "treacherous and unforgiving".
In order to reach the stranded vessel, the Polar Star's crew would have to break through several miles of thick ice, endure winds and navigate through heavy snowfall.
Once Polar Star's crew free the Antarctic Chieftain from the ice, Janas would escort or tow the vessel to the nearest safe harbour.
Australian Longline managing director Les Scott said the crew were safe and the vessel had no hull damage.
Because of the damaged propeller the ship did not have sufficient power to free itself, or push through ice floes to open water, he said.
Mr Scott said the ship, which was licensed to fish for toothfish in the Southern Ocean, was damaged on Saturday when it hit ice.
He said following an underwater inspection, it became clear the vessel would be unable to manoeuvre out of its current position.
"In review of current ice charts and weather forecast, it is expected that ice will continue to build up placing unacceptable risk to both crew and vessel safety, and is unforseeable in the medium term that the ice surrounding the vessel will clear as a result of favourable weather and tidal currents."
RCCNZ search and rescue mission coordinator Greg Johnston also confirmed that the fishing boat's hull was not damaged, and the crew of 26 was not at risk.
There was no spill, he said.
"The crew is safely on board, they have plenty of supplies and the vessel integrity is not compromised.
"There is clear water around the vessel, so the hull is not being squeezed by the ice, but a combination of an unexpected build-up of ice floes two to three metre thick and damage to the propeller means it cannot get back to the open sea without assistance."
