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In a quarterly letter to investors, Bill Miller, the star stock-picker at US asset manager Legg Mason, estimates the fair value for Yahoo to be near $40 per share, versus Microsoft's original offer of $31 per share.

Microsoft "will need to enhance its offer if it wants to complete a deal," Miller writes.

"It will be hard for [Yahoo] to come up with alternatives that deliver more value than [Microsoft] will ultimately be willing to pay," he continues.

"We think this deal is a strategic imperative for [Microsoft] and that [Yahoo] is in a tough spot if it wishes to remain independent."

Miller's comments come as major institutional Yahoo shareholders have been working behind the scenes to get the parties to strike a deal, analysts say. Around 53 of the top 100 big funds in Yahoo hold shares in both companies, according to the most recent shareholder data available from September.

Institutional shareholders hold about 75% of Yahoo's

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stock, versus 10% for company insiders, including co-founders David Filo and Jerry Yang.

Legg Mason Capital Management, the unit of Legg Mason run by Miller, owns more than 80 million Yahoo shares, or 6% of the company, trailing only Capital Research & Management's 11% holding.

Yahoo on Monday turned down Microsoft's bid, now valued at $41.7 billion, saying it did not properly assess the value of Yahoo's vast audience, online advertising investments, cash generation and growth prospects of its overseas holdings.

Microsoft responded the same day by saying its offer was "full and fair," but stopped short of saying it would not raise its price.

Microsoft also said it reserved the right "to pursue all necessary steps" without specifying if it plans to take its bid straight to Yahoo shareholders.

Analysts expect Microsoft to raise its bid to at least $35 a share, but some believe it could be persuaded to go as high as $40.

Analyst Jordan Rohan says major funds are likely to grow impatient with Yahoo to get a deal done if Microsoft raises its bid a few dollars to the mid-$30s-a-share level and sweetens the cash portion of its existing offer.

"The more vocal funds are almost threatening Yahoo that they better take the next offer," Rohan says.

Yahoo shares are now trading at a 2% premium to Microsoft's cash-and-stock deal, indicating investors expect Microsoft to raise its bid.