The director hopes to put it on show by March 24, to coincide with a visit by Pope Francis, a fierce defender of migrant rights.
Inarritu plans to use the northern Italian city as a launchpad for exhibiting the boat in sites around the world, the daily said.
The heavily overcrowded vessel capsized in pitch darkness on April 18-19, 2015 after running into a freighter that was racing to its aid.
It was the Mediterranean's worst disaster since World War II.
The migrant vessel's Tunisian captain was found guilty of multiple manslaughter Tuesday and sentenced to 18 years in prison. His Syrian first mate got five years.
While prosecutors put the number of dead at around 700, forensic scientists counting body parts said it was closer to 900.
Italy's navy had the grisly task of raising the corpse-packed vessel from the seabed this year after the government promised to give the victims decent burials as a symbol of respect for all migrants who have died trying to reach Europe's shores.