The talks have been ongoing for several months, the Journal reported, as Alphabet seeks industry partnerships, offering a deal to sell self-driving car technology.
Alphabet and Fiat Chrysler declined to comment.
Fiat Chrysler has been talking with many players outside the car sector about possible collaborations, as car technology has become a prime area of interest for Silicon Valley companies including Alphabet's Google, which has built a prototype self-driving car.
Earlier this week, Volkswagen Chief Executive Matthias Mueller said the car maker is in talks with external partners to start new digital mobility businesses but added these talks do not involve Apple or Google.
Speaking at a press conference to discuss full-year results in Wolfsburg on Thursday, Mueller said the company was looking for ways to expand its offering in the area of digital mobility services.
"Please understand if I cannot name these companies, but we are not in talks with Apple or Google," Mueller said.
Mueller also said he could not estimate how long it would take to resolve regulatory issues with authorities in the United States, who would first have to receive results of the internal investigation it has commissioned from law firm Jones Day, which is expected to finish its work by the end of the year.
© Thomson Reuters 2016
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