* Shares gain on speculation of Pfizer return later in year
* AstraZeneca rebels need 5 percent support to call EGM
* No realistic prospect seen for deal by May 26 deadline
* But talks could restart in August after cooling-off break
By Ben Hirschler and Anjuli Davies
LONDON, May 21 (Reuters) - Pfizer's chances of striking a deal to buy AstraZeneca in the coming days look vanishingly small, but the notion it could return later this year is propping up the British drugmaker's shares.
The stock rose 3 percent on Wednesday, despite AstraZeneca insisting on Tuesday there wasn't the slightest chance of Pfizer's $118 billion offer being increased by a May 26 deadline set by UK takeover rules.
While Pfizer agrees it cannot raise its final offer of 55 pounds a share, its advisers have been urging investors to speak up against AstraZeneca's decision to reject its proposal, according to several people familiar with the matter.
One suggestion now circulating is that disgruntled AstraZeneca shareholders could call an extraordinary general meeting (EGM) to put Pfizer's offer to a vote. The support of just 5 percent of shareholders is needed to call such a meeting.
Even if shareholders wanted to revive the bid - or oust the board - an EGM would not come in time to rescue the current process before the takeover rules deadline, but they could force AstraZeneca to open communications with Pfizer in late August, after a compulsory three-month cooling-off period.
"Some of the more active hedge funds, instead of selling out are buying in," said one hedge fund investor. "There has been sufficient shareholder dissatisfaction about this deal that investors can use that to get a favourable outcome further down the road."
The only way a deal could be salvaged this month would be for AstraZeneca Chairman Leif Johansson and his board to make a complete U-turn and recommend Pfizer's current 55-pound offer, which looks out of the question.
More leading shareholders spoke out publicly on the deal on Wednesday, but they didn't speak with one voice, underlining the challenge facing the Pfizer camp in trying to stir an investor rebellion.
Threadneedle Asset Management came out in support of AstraZeneca's stance, while investment and insurance group AXA said the board should not have prevented Pfizer's offer being put to investors.
The AXA view was echoed by Legal & General, according to the Wall Street Journal. An L&G spokesman confirmed to Reuters that the fund manager had talked to both companies but declined to comment further.
To date, investors representing around 10 percent of AstraZeneca's share base have spoken out against the board's decision, with a similar number broadly lending their support, according to Thomson Reuters data.
At more than 44 pounds, the shares remain well short of Pfizer's offer but a fair way above the undisturbed price of 37.82 pounds seen before news of Pfizer's interest emerged in mid-April.
A recent run of favourable clinical trial news about AstraZeneca's new drugs has also supported the stock, with UBS issuing a note on Wednesday setting a price target for the shares of 50 pounds, without a Pfizer deal.
Analysts at Barclays, who have a 40 pounds target, said in a note that the market was pricing in a probability of around 15 percent that there would eventually be an agreed deal with Pfizer valuing AstraZeneca at some 60 pounds.
The U.S. company's ambitions to create the world's largest drugmaker - and slash its tax bill in the process - appeared within reach at one point in talks between the two sides last weekend, with AstraZeneca indicating a desired price of 58.85 pounds.
But AstraZeneca's Johansson told Reuters on Monday that Pfizer had closed down discussions after a telephone call lasting more than an hour on Sunday and had surprised AstraZeneca by issuing its final offer later that night. (Reporting by Ben Hirschler; Editing by Will Waterman)