The broadcaster, citing sources familiar with the matter, added that the boss of JLR owner Tata Motors was expected to fly into Britain next week to finalise the deal and meet with Prime Minister Rishi Sunak.
The factory will be built in Somerset, southwest England, after the site beat off competition from Spain, according to the report.
The deal has not yet been signed but preparations are underway over how to present the agreement, the sources told the BBC.
The UK government did not respond to a request for comment.
The Financial Times newspaper had reported earlier this year that Tata had requested 500 million pounds ($603 million) from London to help it build the plant in Somerset.
Environmental campaign group Greenpeace welcomed Wednesday's report.
"Securing this gigafactory was critical to ensuring the UK even has a car manufacturing sector going forward," said Greenpeace UK policy director Doug Parr.
"But the thousands of jobs it will create demonstrates the huge advantages that come with investing in home-grown green tech."
Britain plans to ban the sale of new high-polluting diesel and petrol cars from 2030, forcing its car manufacturing sector to switch production to electric vehicles.
That target is part of its long-standing goal to achieve net zero carbon emissions by 2050 in order to help tackle climate change.
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