Marchionne, the chief executive of both automakers, told reporters in Bologna, Italy, that Fiat should reach a 30 percent stake in the US automaker within 30 to 60 days. Fiat now has 25 percent.
Under the bailout agreement signed with the US Treasury in 2009, Fiat must sell Chrysler vehicles through 90 percent of its dealers in Latin America to increase its stake in the firm.
Chrysler has had problems with local franchise laws, particularly in Brazil, which has slowed the process. But a top Chrysler executive said Thursday that a solution is near.
That solution would call for Chrysler to sell its vehicles in Latin America under the Fiat brand, clearing the way for Fiat to boost its stake in the US automaker to 30 percent.
"The spirit was for us to be able to expand our reach and our growth within the marketplace and there are different ways of achieving that," Michael Manley, head of Chrysler's international operations, told reporters at Chrysler's Auburn Hills, Michigan, headquarters on Thursday.
"As we've looked at the situation, I think we've found the best way of achieving that," Manley added.