The Italian Costa Allegra, carrying more than 1,000 passengers and crew members, began drifting without power on Monday after a fire in its generator room.
The coast guard said on Tuesday that authorities were making arrangements to evacuate those on board the Costa Allegra to the island of Descroches, and for their subsequent transfer to the Seychelles' main island.
Srdjana Janosevic, the Seychelles' presidential spokeswoman, confirmed that the French vessel had reached the ship and that it was towing the Costa Allegra to an island.
"We will evacuate them from the ship. [Those on board] will have time to rest on the island, to call their families and so on, and then they will be transfered to the main island of Mahe."