The unions claim Fiat is to close the Fiat Powertrain plant at Arese near Milan and instead source six-cylinder engines from General Motors.
Fiat has yet to comment on the matter, but the unions say the new engines will be made by GM in Australia.
The news comes a week after GM pulled out of an agreement to buy Fiat.
GM had to pay former partner Fiat €1.55bn (£1.1bn) to get out of a deal which could have forced it to buy the Italian carmaker outright.
Fiat and GM also ended their five-year alliance and two joint ventures in engines and purchasing, but did agree to continue buying each other's engines.