The statement rebuff's Volkswagen Group, which said last week it had its eye on the brand for a possible purchase.
"Volkswagen are welcome in our country and I'll work to facilitate their entry into Italy, but Alfa Romeo is not for sale," Marchionne said.
Italian news agency ANSA reported that a Volkswagen spokesman had confirmed the company was interested in the purchase.
"It's no secret that we consider Alfa Romeo to be an interesting marque," spokesman Eric Felber said.
But Volkswagen could take the rejection, he said.
"You can be sure that we have lots to do with the 12 marques we already have," Felber said.