Up to 31 British nationals are stranded on the Costa Allegra, the ship which went adrift in the Indian Ocean after a fire and power failure.
No passenger injuries have been reported, and the owner of the ship, Costa Cruises, maintained that the ship was in good condition.
Costa Allegra was being towed away by a French fishing vessel to Desroches island, southwest of Seychelles, the BBC said.
Passengers will be transferred to Mahe, Seychelles' main island, by tug.
The power failure has left the ship with no airconditioning or cooking facilities and there are fears radio contact could be lost.
The ship was carrying more than 1,000 people when a fire in the generator room of the cruise vessel caused a blackout.
Costa Allegra was en route from Madagascar to the Seychelles.
It belonged to the same fleet as Costa Concordia, which capsized off the Italian coast on 13 January, claiming 25 lives.
Relatives in the UK can contact the company's helpline on 020 7940 3300.