Among those who have already signed up for the trip are a London banker and a doctor from Missouri, the Telegraph reported.
Deep Ocean Expeditions are hoping to take 80 people to the ship on the centenary of its sinking in 2012.
However, just two visitors would be able to go down at a time and it would take two hours to descend to the wreck, that was discovered in 1985.
The spot is also the resting place for 1,517 people who died on April 14, 1912.
Rob McCallum, expedition leader of Deep Ocean Expeditions, said it would be the only time the firm took tourists to the spot.
"We never set out to be a retail travel company. Next year will be a poignant year to make the trip. It's a good time for us to sign off," he said.
Between the two parts of the broken ship, the ocean floor is strewn with bottles, cups, knives and leather suitcases.