"What we're doing is talking intensively with Tata to make sure they do everything they can to make sure this is a serious sales process," Cameron said while addressing the House of Commons yesterday.
"We need to work intensively with Tata and with those buyers to get that list down to those who are really seriously intending to bid for the business. It's a very short time table," he told MPs.
"Does the Prime Minister really think that that's a realistic time frame and that there'll be a credible process of due diligence? And what steps is the Prime Minister taking to ensure that Tata Steel delivers on its promise to be a responsible seller?"
The mid-June time-frame has been the general estimate on the sales time-line but a 'Financial Times' report today suggests that the company may extend this till after the EU referendum scheduled for June 23, when Britain votes on whether to remain in and leave the European Union.
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Two formal bids are in the running to acquire Tata Steel's UK assets so far - one by Indian-origin businessman Sanjeev Gupta's Liberty House group and the second by Excalibur Steel UK Limited,a management buyout (MBO) team of former Tata Steel staff who have the backing of the Welsh government.
In his first interview since he took a leave of absence from Tata Steel UK to head the MBO, Excalibur Steel UK CEO Stuart Wilkie said he sees getting employees to invest around 10,000 pounds each in the business as a "moral element".
Liberty's bid is based on the company's 'Greensteel' business model and would involve a transition from steelmaking in blast furnaces to recycling steel in electric arc furnaces over time.