The job cuts would affect three plants in Italy and represent 15 percent of the 30,000 workers employed on assembly lines in the country, the newspaper said.
The Fiat group employs just over 80,000 people in Italy and 190,000 worldwide, according to its latest financial report.
Fiat is due to unveil its 2010-2014 plan on April 21.
La Repubblica also said Fiat would cut the number of car models produced to eight from 12 and boost Italian production to 900,000 cars, representing a 50 percent increase.
In the United States, where Fiat has taken a stake in struggling carmaker Chrysler, the Italian group would seek to produce seven models using the brands Fiat, Lancia and Alfa Romeo for a total production of more than 350,000 units.
Fiat was not immediately available for comment.
(Writing by Lisa Jucca; Editing by David Holmes)