Marchionne left last night, the source said.
He may have a meeting with Chrysler executives in New York, where an auto show is currently underway.
Fiat and Chrysler are trying to finalize a partnership by the end of April which would help the U.S. car maker avoid bankruptcy.
On Wednesday, Chrysler Vice Chairman Jim Press said his company was working around the clock to complete the deal.
He took a drive in a Fiat 500 small car at the auto show in New York on Wednesday.
The company has been given until the end of this month to complete the deal with Fiat by a U.S. presidential task force.
Marchionne was in the United States for discussions at the beginning of this month.
The framework of the deal is for Fiat to take a stake in Chrysler that would start at 20 percent in return for access to its small-car technology and vehicle platforms.
(Reporting by Gianni Montani, writing by Jo Winterbottom)