Shares of Amylin Pharmaceuticals rose as much as 51% on Wednesday after Bloomberg News reported the company rejected a $3.5 billion unsolicited takeover bid from Bristol-Myers Squibb.

Bristol-Myers proposed an acquisition at $22 a share in a letter to Amylin, which the board turned down last month, according to Bloomberg, which cited two people with knowledge of the matter.

Bloomberg said Bristol-Myers has not approached Amylin, which makes the diabetes drugs Byetta and Bydureon, since the rejection. Spokeswomen for Bristol-Myers and Amylin said they "do not comment on market rumors or speculation."

Amylin has been considered a possible takeover target for some time, with some analysts speculating AstraZeneca might be an interested buyer.

Tim Anderson an analyst at Sanford Bernstein said recently he believed an Amylin acquisition would fit well and work financially assuming AstraZeneca paid a 30% premium to the stock price plus $1.5 billion for an outstanding promissory note and convertible debt, which would have valued Amylin at $4.5 billion.

The diabetes sector is one of the fastest-growing in the drug industry due to rising rates of obesity. More than 300 million people worldwide suffer from diabetes, including nearly 26 million Americans. They run a high risk of heart disease, stroke, kidney failure, blindness and limb loss.

Joshua Schimmer, an analyst at Leerink Swann, said in a research report on Wednesday that he believes Bristol-Myers "may not be the strongest bidder, given its weaker presence in the diabetes space in Europe and emerging markets."

Companies like AstraZeneca could drive greater value of Amylin's diabetes franchise on a global basis.

"As such, we believe shares have a reasonable floor, the company has a legitimate chance of finding a higher bidder," he said.

In November, Amylin ended a nearly decade-long partnership with Eli Lilly. Amylin's shares fell more than 11% on that news amid concern the company might not be able to market the products on its own. Amylin and Lilly introduced Byetta in 2005. Bydureon, a longer-acting version, was approved recently.

The dissolution of Amylin's partnership with Lilly made Amylin responsible for selling its products in the United States, while leaving the company to find a new partner outside the United States.

Schimmer said he believes the "leaking" of the Bristol-Myers story serves the purpose of tying Amlyin's hands and preventing the company from forming a partnership outside the United States instead of a sale.

"At this valuation and with this information in the public domain, management will have a hard time justifying an extreme level of downside to shares, which would almost certainly come from an ex-U.S. partnership," he said.

Bernstein's Anderson said on Wednesday in a research note that while it is still plausible that AstraZeneca could pursue Amylin, what would shoot down the idea of Amylin as an acquisition target is if Amylin does indeed sign up a partner to help market its products outside the United State.