Marchionne confirmed the joint-venture vehicle's name during a question and answer session with members of the European motoring press.
When FCA decided to rejuvenate Alfa as a made-in-Italy, rear-wheel drive brand, a decision was made to turn FCA's version of the MX-5 into a Fiat or Abarth. Alfa will instead develop its own convertible model from the rear-wheel drive platform underpinning its upcoming BMW 3 Series fighter.
With the base vehicle confirmed as a Fiat model, AutoExpress is reporting that a more powerful Abarth version is still on the cards.
The last 124-badged convertible, the Fiat 124 Sport Spider (above), was sold by Fiat between 1966 and 1982, and was a Pininfarina model until 1985.
Featuring a simple front-engine, rear-wheel drive layout, the 124 Sport Spider was powered by everything from a 66kW 1.4-litre to a 99kW 2.0-litre engine.
The new Fiat 124 Spider isn't expected to launch until 2016.