Fiat's press service declined to comment on the reported conversation.
An initial public offering (IPO) for Ferrari "appears increasingly likely in the next 12-18 months," analysts from US bank Morgan Stanley said in a note.
The analysts also cited Marchionne as saying that Fiat and US auto firm Chrysler would eventually merge after Fiat after the IPO.
Analysts from Germany's Deutsche Bank said: "Marchionne aims to have one single listed unit between Fiat and Chrysler before the end of 2014."
After the publication of the analyst notes, shares in Fiat shot up 3.08 per cent to 13.38 euros in Milan, where the main index was up 0.43 per cent.
Fiat holds a 20-per cent stake in Chrysler, which emerged from bankruptcy proceedings in June 2009. Fiat's stake is set to rise to 25 per cent by the end of the year and 35 per cent by the end of next year.
Fiat currently owns 85 percent of Ferrari.