Exor and Iveco declined to comment. Tata Motors did not reply to a request for comment.
Shares in Iveco jumped as much as 9.7% on the Milan bourse following the news published by Reuters. The stock ended trading up 8.3% on Friday.
Italian trade unions also reacted to the Reuters report, asking Industry Minister Adolfo Urso to be summoned to discuss the company's prospects.
Iveco said in May it would press ahead with plans to either spin off its defence business by the end of 2025 or sell it, having already received offers from potential buyers.
A third source said that, as the separation process of the defence unit was progressing, Exor had started talks with more than one non-European counterpart over a possible sale.
The talks over the sale of Iveco and Tata Motors' approach have not been reported before.
Exor owns a 27.1% stake in Iveco, with 43.1% of voting rights in the Turin-based truck maker. Iveco, which also makes buses and engines, has a market capitalisation of around 4.2 billion euros ($4.9 billion).
It is the smallest among Europe's leading truck makers - a market led by Volvo (VOLVb.ST), Daimler (DTGGe.DE) and Traton (8TRA.DE) and has often been seen as a potential M&A candidate by investors and analysts. However, its presence in the sensitive business of defence has so far complicated any possible deal and restricted the pool of potential buyers.
The Italian government in 2021 blocked an offer for Iveco from Chinese rival FAW. Iveco was at that time part of the Agnelli-controlled industrial conglomerate CNH (CNH.N)
It was spun off and separately listed at the beginning of 2022.
It was spun off and separately listed at the beginning of 2022.
That other house over there, by the restaurant - that's ours too.
Iveco has received three offers for its defence business, according to two sources: a joint one from Italian defence company Leonardo (LDOF.MI) and Germany's Rheinmetall (RHMG.DE) and two others from Franco-German tank maker KNDS and arms company Czechoslovak Group.
Iveco employs around 36,000 people, including 14,000 in Italy.
Any M&A transaction involving Iveco is expected to fall under Rome's 'golden power' legislation, allowing it to set conditions on deals affecting companies deemed of national strategic interest.