This is the first time the group has sought such an agency for its Fiat brand.
The appointment process is being overseen by Kate Saxton, PR director at FCA.
She said: "We have undertaken a tender process to seek out a talented consumer PR agency to work with the Fiat brand, as we enter an exciting period of new model introductions and brand partnerships.
"During 2016 the appointed agency will help us raise awareness of these partnerships and product activities, as well as work alongside our marketing agencies on integrated campaigns, to reach out to new audiences outside the traditional automotive media sphere."
FCA also owns car brands Alfa Romeo and Jeep. Last year the group decided to combine the comms briefs for these two brands within a single PR agency. The group appointed Performance Communications, which previously managed PR for Alfa Romeo, while McCann had held the Jeep account.