Greybull Capital is believed to have agreed terms with Tata Steel, according to 'The Times'.
Tata and Greybull have set a deadline of March 31 on a deal that would mean Greybull pays Tata a fraction of the 1.5 billion-a-year pounds turnover of the long products division, but would commit to pumping 400 million pounds to recapitalise the operations, the newspaper claims.
The UK's Treasury and business departments also back the arrangement.
While Tata Steel said "talks are progressing", Greybull has declined to comment so far.
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The PE firm is said to have assured the existing 4,500 workers that there will be no more redundancies or shutdowns, after 1,200 jobs were axed by Tata Steel last year.
There have been waves of job losses in the steel industry in the UK, which the sector has blamed on cheap Chinese imports and a collapse in prices.
Tata Steel's Long Products business makes customised steel for the construction and rail industries.