The negotiations were ongoing on Tuesday.
Parallel talks are taking place with Jingye, the Chinese owner of Scunthorpe-based British Steel which is also preparing to close its blast furnaces, but are less advanced.
It comes after ministers, including Business Secretary Jonathan Reynolds and Welsh Secretary Jo Stevens, vowed to get a better deal for Port Talbot workers.
During the general election campaign, they warned Tata not to proceed with any irreversible decisions; and after winning power in July immediately began formal talks with the steelmaking giant.
Mr Reynolds is expected to make a statement to the House of Commons about the new agreement on Wednesday.
One person close to the discussions insisted that the Labour Government had secured meaningful changes to the prior agreement struck with the Conservatives.
They added: “There are marked improvements – it is not just the £500m.”
However, with plans to close the ageing blast furnaces already well advanced when the election was called, the source claimed ministers and the unions were limited in what they could realistically achieve.
“The inaction under the last government means we were to some extent timed out,” they admitted. “But under those circumstances, what has been achieved is good.”
Another person added: “There are commitments on future investment that were not there before.”
A key part of the new deal is expected to be a stronger commitment to helping former Port Talbot workers retrain or find new work.
That is reportedly at the centre of negotiations ahead of Wednesday’s announcement, but it is unclear what specific concessions ministers have secured.
Tata’s commitments on future investment are also likely to be conditional on a favourable business case, although Labour has made clear that the company could apply for further support through the £2.5bn green steel transition fund.
Last month, the Government also said it was pressing ahead with the “immediate release” of £13.5m from a £100m fund set up to support workers losing their jobs.
Labour had previously criticised the Conservatives for not disbursing money quickly enough. The Government has contributed £80m and Tata another £20m to the fund, but as of May no cash had been spent.
On Tuesday, the Department for Business and Trade said: “Steel is vital for a vibrant, secure economy.
“Our steel sector needs a government working in partnership with trade unions and business to secure a green steel transition that’s both right for the workforce and delivers economic growth.
“Decarbonisation does not mean deindustrialisation, and we will be working to safeguard jobs as part of these negotiations, securing the future of steelmaking communities for generations to come.”
Meanwhile, the Welsh Conservatives claimed Labour had “come to its senses” and effectively adopted the deal negotiated by the previous government, the BBC reported.
Charlotte Brumpton-Childs, GMB national officer, added: “Since the election the Government has had extensive discussions with Tata and has strengthened investment assurances.
“Tata has now given binding commitments to work quickly to invest and unlock further investments.
A spokesman for Tata said it would not be appropriate to comment in advance of any formal announcement.