Giampiero Borghini, Marco Formentini, Paolo Pilleteri and Carlo Tognoli are being investigated for manslaughter and grievous bodily harm, Ansa reported, citing sources.
The period over which the mayors were in office spans between 1976 and 1997.
Carlo Fontana, the former superintendent of Teatro alla Scala, which was built in 1778, is also being investigated. Fontana was in the role from 1990 to 2015.
The famous opera house, which has hosted some of the greatest names in Italian opera, including Bellini, Rossini and Verdi, underwent a major renovation between 2002 and 2004.
In 2009 a seating area in an upper gallery was closed off after asbestos was found in the ceiling.
The building was severely damaged by bombing during the Second World War in 1943. It was rebuilt and reopened in 1946.
The latest asbestos probe comes after 11 former managers at the Italian tyre manufacturer, Pirelli, were convicted of manslaughter in July over the asbestos-related deaths of 24 workers.
The workers contracted tumours linked to asbestos exposure while working at the company’s factories during the 1970s and 80s.