The blaze started on the 852-passenger Sorrento (built 2003) on Tuesday as it was travelling off Palma de Mallorca and Valencia.
Three tugs have reached the ship 22 miles from land, and were carrying out hull-cooling operations.
Local media said investigators had been lowered on to the vessel by helicopter.
It still has 750 tons of bunkers on board.
The ro-pax could be towed to Palma.
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