Ilva, privately-owned by the Riva family, is Europe's largest steel plant by output capacity and is of strategic importance to the southern European steel sector, where it supplies carmakers and other manufacturers.
The Taranto plant, however, is at the centre of an environmental scandal which led the Italian government to place it under "special administration", a procedure designed to save large companies and avoid big job losses.
JSW Steel, controlled by Indian tycoon Sajjan Jindal wrote a letter to Ilva's special commissioner Piero Gnudi to express interest in Ilva, according to the sources.
A JSW delegation is expected to visit the plant, one of the largest employers in the southern Italian region of Puglia, in the next few days.
Ilva declined to comment.
JSW did not immediately reply to a request for comment.
ArcelorMittal, the world's largest steelmaker last month sent a letter to express its interest in Ilva to Gnudi and is expected to propose an industrial plan for the plant by the end of September, according to sources.
JSW is also in talks to buy parts of another steel plant, Lucchini, Italy's second-largest.