No, nothing of this sort is happening in India. After the split (sort of!) with Tata, Fiat would handle its own interests itself here.
But there is an interesting preposition that is reportedly saying that Anand Mahindra of Mahindra & Mahindra has shown keen interest in buying ‘a’ brand of Fiat SpA. Now this ‘a’ could be any of the many brands that Group Fiat owns. Basically, Mahindra wants to have a greater presence in Europe and through this acquisition they want to achieve just that.
Fiat is in deep trouble and has plans to shut down a few of its production plants in Italy.