FCA Chief Executive Sergio Marchionne said last month that he would spin off Ferrari, sell a 10 percent stake via a public offering and distribute the rest of FCA's stake in the luxury sports car brand to its shareholders.
As a consequence, the Agnelli family will emerge as the largest shareholder in Ferrari after the spin-off. A loyalty scheme could tighten the Agnellis' grip further and increase their influence on Ferrari's future strategy.
Read MoreDealer offers free cars if it snows on Christmas
The spin-off announcement rekindled speculation that the Agnelli family may want to form a pool of luxury brands around Ferrari, including other opulent Italian names from outside the automotive sector, to rival groups such as France's Kering and LVMH.
Marchionne said last month that carmaking is "almost incidental" to Ferrari, which he sees more as a luxury stock.
But Elkann, a scion of the Agnelli family who also heads Exor, dismissed the idea of a luxury conglomerate, saying that Exor's plan is to give Ferrari the chance to develop its own growth strategy.
Elkann added that there are no plans at this stage to replace Ferrari Chief Executive Amedeo Felisa.
Ferrari has undergone several management changes in recent weeks, with long-time Chairman Luca Cordero Di Montezemolo pushed out last month and a new Formula One principal appointed this week.
Read MoreRussians dumping rubles for...Rolls Royces?
Milan-listed FCA shares were down 0.2 percent at 10.05 euros by 1324 GMT, against a 0.8 percent fall in Milan's blue-chip index. The stock has gained nearly 45 percent since moving its primary listing to New York on Oct. 13. (Get the latest quote here.)