Recall rejected the $7 a share offer on Monday and, in an unusual move, published estimates of the synergies Iron Mountain could extract from a merger and the implications for the offer price.

In a statement to the New York Stock Exchange Iron Mountain chief executive William Meaney said there is a major gap in estimates and expectations between bidder and target.

"We believe our proposal accurately reflected the value creation potential of the combined businesses – and an appropriate allocation of the potential synergies between shareholders of both companies," he said.

"We see little point in having further discussions with Recall regarding a purchase of the company given their estimated values."

Recall thinks that combining the two businesses would create $US3.9 billion of additional value and its shareholders would get less than 5 per cent of that extra value at $ 7 a share.

The company, which was spun out of Brambles last year, estimated Iron Mountain could extract $US250 million in annual synergies from the deal.

Based on $US250 million of synergies, Recall estimates a $14.01 a share offer would give its shareholders 50 per cent of the created value. Recall also said it expects its own earnings growth and margin expansion could deliver an $11.15 share price in three years.

Recall boss Doug Pertz said on Monday that he does not think Recall is entitled to 50 per cent of the synergies. He insisted he is not drawing a line in the sand on value.

But Mr Meaney said his company is "very surprised" by the big estimates.

"Iron Mountain's estimate of net synergies is substantially lower than Recall's estimate, which additionally, does not include the substantial time and transaction costs required to realise those synergies," he said.

The $7 a share offer to acquire Recall by way of a scheme of arrangement comprised$404 million in cash and $1.82 billion of Iron Mountain stock.

The bid followed an initial proposal of $6.75 a share made on December 5.

"Despite the increase in the offer price...there remains a significant difference in valuations by both parties. Consequently we believe a deal is unlikely," Citi analyst Anthony Moulder said.

Recall's biggest shareholder Deccan Value Investors (DVI) supported the board's decision to reject the bid.

"DVI considers that the proposal... does not reflect the current value of Recall's business or take into account the significant synergies available," DVI founder Vinit Bodas said.

DVI owns 13.25 per cent of Recall and manages around $2 billion.

CIMB analyst Mark Williams said Iron Mountain could possibly lift its bid to almost $9 a share.

But he warned Iron Mountain may offer little more than $7.50 or $8 and said there is a risk the bidder walks away without increasing its bid at all.

"Iron Mountain is not in a competitive bidding process as it is the only party that can generate substantial cost synergies through an acquisition of Recall," Mr Williams said.

Mr Williams thinks Recall's fundamental value is $5.52 a share.

JP Morgan analyst Andrew Steinerman said Iron Mountain could "raise its bid incrementally" but is likely to remain disciplined given the focus on reducing debt and growing dividends.

Iron Mountain is carrying around $US4.3 billion in debt.

Recall shares shed 5.2 per cent to $7 on Tuesday. The stock surged 15.3 per cent to a record high of $7.38 on Monday when news of the Iron Mountain takeover bid became public.