Shares in Fiat jumped 5 percent to 7.98 euros on the news, while VW's stock was 1.5 percent lower at 186.70 euros.
Both VW and Fiat declined to comment. The Agnelli family's holding firm Exor, which owns a 30-percent stake in Fiat, had no immediate comment.
Manager Magazin said VW and Fiat's owners were still far from reaching an agreement on a possible price for the Italian carmaker.
By purchasing Fiat Chrysler, VW is hoping to use Chrysler's U.S. distribution network to help solve its own problems in the world's No. 2 auto market where sales of the core VW car brand have been flagging, it said.
VW Chief Executive Martin Winterkorn told the carmaker's March 13 annual news conference that VW has no plans at present to expand the group through further acquisitions as it is focusing on integrating its 12-brand network.
VW, which had cash reserves of almost 18 billion euros ($24.36 billion) at the end of March, has repeatedly expressed an interest in Fiat's Alfa Romeo brand despite rebuttals from Fiat CEO Sergio Marchionne.
(Reporting by Andreas Cremer; additional reporting by Agnieszka Flak in Milan; editing by Maria Sheahan and Jason Neely)