Fiat received the 20-percent stake in Chrysler in 2009 as payment for assuming operations at Chrysler, which emerged from bankruptcy in June.
Under the conditions of the deal, Fiat can increase its ownership in Chrysler if it shares small-car technology and expands the U.S. car maker's international presence, The Wall Street Journal reported Saturday.
"I think in the next 24 months at the most we will arrive at 35 percent," Fiat Chief Executive Sergio Marchionne said Friday at a Fiat shareholders meeting in Turin, Italy. Marchionne also is Chrysler's chief executive officer.
Friday, Chrysler announced it wants to reinstate 50 U.S. dealers it closed last year and was negotiating others in an effort to avoid arbitration. Chrysler last year said it would close 789 dealers, 418 of which have filed for arbitration with the aim of remaining open.