Sergio Marchionne, head of both Fiat and Chrysler, is keen for a deal that would create the world's seventh-largest carmaker, but has not managed to agree a price with VEBA, which is affiliated to the United Autoworkers' Union (UAW) and owns 41.5 percent of Chrysler.
The source said Fiat executives had met VEBA officials, but did not know any further details.
Bloomberg reported earlier on Friday that the meeting followed VEBA's rejection of a higher offer for its stake in Chrysler earlier this month, citing people familiar with the matter.
Fiat and Chrysler declined to comment.
Last month Fiat said a planned stock market listing of Chrysler, which was expected to help settle the long-running spat between the two companies over the U.S. automaker's value, would not take place this year, prolonging uncertainty over Marchionne's chances of buying out the rest of the company.