The three companies tipped to be named are commodities trader Liberty House, management buyout team Excalibur, and Leeds-based private equity fund Endless.
The Indian steel conglomerate has been reviewing up to seven bids since the deadline for submissions passed on 23 May.
It was thought a shortlist could be revealed last week following a Tata Steel board meeting in India.
“We aren’t surprised by the names [that are set to be shortlisted],” said a spokesperson for steelworkers union Community. “These businesses have long looked like the front runners, and those are probably the names we would pick out.”
It’s understood Tata is now working towards 24 June to name a buyer.
The government has been consulting with both Tata Steel and prospective bidders over recent months.
There have recently been a flurry of reports that Tata will not go through with a sale of the business and will hold onto its UK assets, with the government taking a minority equity stake of up to 25 per cent.
Tata insists the sale process is moving forward.
The four firms expected to miss out on the shortlist are turnaround specialist Greybull Capital, Indian steel producer JSW, Chinese steelmaking giant Hebei, and US billionaire investor Wilbur Ross.
Yesterday Greybull completed its £1 purchase of Tata’s Scunthorpe steelworks, re-branding it as British Steel – a name not seen since 1999.
The Scunthorpe works made a loss of around £100m last year.