British Steel was part of Tata Steel Europe and was sold to Greybull Capital in 2016.
Sources close to the development told Moneycontrol that the Sajjan Jindal-led company has been approached by British Steel's representatives.
"JSW Steel is considering the option, as British Steel could come at a very low price and wouldn't put pressure on its leverage. At the same time, a possible deal will give JSW Steel access to steelmaking facility in developed markets," said a senior executive from the industry.
The deadline to submit bids - earlier June 12 - for British Steel has been pushed to the end of the month to let more suitors come in.
Responding to Moneycontrol's query, its spokesperson said: "JSW Steel doesn't comment on market rumours and speculations."
The country's largest steelmaker has been aggressively expanding its overseas footprints in the last few years. While in the US, it has earmarked an investment of $1 billion to develop assets in Texas and Ohio, in Europe, JSW Steel acquired Italy's Aferpi last year.
British Steel has facilities in the UK, France and Netherlands, and specialises in making long steel used in construction.
In 2016, Tata Steel has sold the assets to Greybull Capital, a private wealth fund, for £1, as part of its attempts to stabilise the operations.
The plants were put together under the umbrella of British Steel, the name given by Greybull Capital. The name was part of the bid to bring back glory of UK's steel industry. The UK operations of Corus, which was bought by Tata Steel in 2007, were earlier called British Steel.
While the units turned profitable a year later under the new owner, conditions soured in 2018. This year in May, the company was put into compulsory liquidation after talks between the UK government and Greybull Capital over a rescue package collapsed.
The collapse has endangered jobs of more than 5,000 workers, and attempts are being made to reach out to interested parties, including steelmakers and PEs, across the world.Apart from JSW Steel, South Korean steelmaker POSCO is also said to have been approached.