A ballot of union members closes on Wednesday and is expected to deliver resounding support for the deal, 'The Sunday Times' reported.
The four unions - Community, Unite, GMB and Ucatt - called off a strike last month after the Indian steel giant agreed to retain a modified final-salary pension scheme.
The unions have recommended that staff accept the deal.
Tata argued that reforms to the British Steel Pension Scheme, which has about 135,000 members and a deficit of more than 2 billion pound, are vital if the company is to return to profitability.
The Scunthorpe site is the largest with about 4,000 workers.
Tata bought the Anglo-Dutch steelmaker Corus in 2007 for 6.2 billion pound, before the financial crisis.
It had been in talks to sell the division to American tycoon Gary Klesch but those discussions stalled and the commodities billionaire lost exclusive negotiating rights.
Tata is reportedly looking at other options, including a possible sale to management, and could force through heavy cost cuts and job losses if a deal fails to materialise, the newspaper claimed.
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