The Italian company said it was offering the United Auto Workers Retiree Medical Benefits Trust $198 million for another 3.3 percent of the company that it began buying when Chrysler went into bankruptcy in the summer of 2009.
The Detroit Free Press reported Friday the purchase, if it goes through, would bring Fiat's stake in Chrysler to 65.17 percent.
There is, however, a major hurdle to overcome before a deal can be struck – a lawsuit between the trust and Fiat that needs to be resolved to settle a disagreement between the two parties over the value of Chrysler shares.
The difference is large and the final price is expected to be settled by a court in Delaware, the newspaper said.
In July, Fiat offered the trust fund, known as VEBA, $155 million for 54,154 shares. VEBA, however, said the shares are worth about $381 million.
Fiat has an agreement in which it can purchase 3.3 percent at six-month intervals.