Earlier this month, Jingye Group announced a provisional deal to buy British Steel, but the acquisition needs regulatory approvals.
Gupta, who heads the privately-held GFG Alliance, has snapped up steel assets around the world and made repeated offers to buy British Steel.
One of the sources said Gupta was "still interested", but that, if the Jingye process dragged on too long, a rescue plan might at some point no longer be viable.
British Steel's main plant, in Scunthorpe, has been operating as normal, workers say, since it went into compulsory liquidation in May. The British government has been paying the wage bill, which last year was 250 million pounds ($320 million), industry sources say.
Jingye's provisional deal needs regulatory and foreign investment clearance from European jurisdictions, including the European Commission.
A spokesman said the EU executive had not received formal notification of the deal, while a Jingye spokeswoman in China said there were "a lot of procedures" yet to be done.
British Steel's plant at Hayange in France could lead to complications.
French Economy and Finance Minister Bruno Le Maire said he would work to ensure that France's "sovereign interests" and Hayange's importance as a supplier to the French rail operator SNCF were protected.
Gupta has not said how much he would be willing to pay for British Steel, while the Jingye offer is around $50 million, industry sources have said.
The two sources commenting on Gupta said his bid was based on replacing one of the two blast furnaces at British Steel's Scunthorpe site with an electric arc furnace (EAF) that would recycle scrap and emit much less carbon dioxide.
However, EAF technology has higher power costs and employs at least 50% fewer people than a blast furnace.
That would make such an offer politically sensitive as Britain heads into a parliamentary election on Dec. 12, in which the relative lack of high-paid jobs in northern England is expected to influence voting.
It would, however, have long-term strategic benefits. Britain produces around 10,000 million tonnes of scrap steel annually, most of which it exports, while importing iron ore and coking coal to run blast furnaces.
Julian Allwood, an engineering professor at Cambridge University, says Britain's best hope for saving its steel industry and maintaining long-term jobs is to scrap blast furnaces, which he predicts will disappear in any case.