Dutch marine engineer Boskalis said on Friday that it has been appointed to salvage both tankers that were hit in the Gulf of Oman in a suspected attack.
Boskalis said the condition of the Front Altair tanker, carrying a cargo of naphtha, was still worrying, although the fire on the ship had been extinguished on Thursday.
The methanol-carrying Kokuka Courageous was in a stable condition, Boskalis said.
Its crew had been able to return to the vessel, which was being towed to a port in the Gulf region.
The Norwegian-owned Front Altair and the Japanese-owned Kokuka Courageous were both hit by explosions on Thursday, forcing crews to abandon ship and leave the vessels adrift in waters between Gulf Arab states and Iran.
The United States has blamed Iran for the attacks that drove up oil prices and raised concerns about a new US-Iranian confrontation, but Tehran has denied all allegations.
Shortly after the incidents the insurers of both vessels appointed Boskalis subsidiary Smit to salvage the vessels and their cargo, the company said without providing further details.