The likeliest new location for Fiat would be the Detroit area, specifically Auburn Hills, Mich., which is already the home of Chrysler, the Chicago Tribune reported Friday.
On the other hand, Fiat might chose another U.S. city, the newspaper said.
Fiat owns 58.5 percent of Chrysler. Both are run by Chief Executive Officer Sergio Marchionne, who has said in reference to a new headquarters, "The thing that would certainly be the single largest factor in our consideration is the adequacy of the capital markets to support operations going forward."
"And I will leave it to you to decide where that market is," he said.
Marchionne also said recently that "Europe is becoming a less and less relevant fact in the scheme of things," balancing out that statement with a qualifier. "That is not to take away from our historical roots," he said.
It is clear, however, that moving Fiat's headquarters out of Italy after 114 years of business would be an unpopular move among Italian unions and politicians.
Production decisions would likely be little changed if Fiat's administration center left Italy. But Fiat's research and development focus could shift to take advantage of Michigan's status as the epicenter of the automobile industry.
"To say that Fiat is pretty entrenched in Italy would be an understatement," said Mike Wall, director of automotive analysis for IHS Automotive. "There would be a healthy resistance to this from Fiat workers, Italian shareholders and the Italian government," he said.
On the other hand, "you look at where Fiat's profits are being generated," Wall said.
From that angle, the numbers are clear. Fiat sold 1.1 million vehicles in Europe in 2012 and 1.7 million in the United States, IHS Automotive Consulting said.
"The center of gravity of the industry is here, both in leadership and technology," said David Cole, an automotive engineering professor at the University of Michigan.
Some analysts, however, have an alternative theory to explain Marchionne's statements.
As he frequently complains about production problems in Europe, Marchionne may be using the threat of leaving Italy as a means of pressuring unions and politicians to grant Fiat more favors, some analysts say.