Reuters said it was not clear whether Allergan had put forward an offer and the company did not immediately respond to requests for comment.
The Japanese firm now faces a bidding war for Shire as Botox maker Allergan is said to be in talks to buy the company, Reuters reported, citing sources.
Shire was founded in Basingstoke, Hampshire, in 1986, but the company has scaled back its presence in the United Kingdom and most of its operations are in the US. The firm offers products in therapeutic areas, including hematology, genetic diseases, neuroscience, immunology, internal medicine, ophthalmology, and oncology.12.5 is the P/E ratio.
The largest United Kingdom takeover closed in 2015 when Anheuser-Busch InBev bought SABMiller for more than $130 billion, including debt.
Takeda, led by Frenchman Christophe Weber, has been actively looking overseas for acquisitions. A few months earlier, Takeda also sought to acquire the Salix Pharmaceuticals unit from Valeant Pharmaceuticals worldwide, but talks collapsed when the companies couldn't agree on a price.
FILE PHOTO: Vitamins made by Shire are displayed at a chemist's in northwest London, Britain, July 11, 2014. RBC Capital Markets maintained it with "Buy" rating and $192.0 target in Monday, February 5 report.
An acquisition of Shire would give Allergan heft in the coveted rare diseases space at a time, when CEO Brent Saunders is seeking to cement its status as a purveyor of innovative drugs.
For Takeda, the deal would mean a expanded presence in the U.S. - Shire collected about 66% of its revenue from the U.S. previous year.
WWE Announcement on Bruno Sammartino Passing Away, Triple H Remembers Bruno
Sammartino passed away in his adoptive hometown of Pittsburgh following an illness, surrounded by family. Over the course of his career, Sammartino was the headlining act for a record 187 sold out appearances.
The most recent offer was for £28.75 in Takeda shares to be traded on the Japanese stock exchange, and £17.75 in cash, which would have given Shire shareholders a 51% stake in the combined company.
Shire's board has unanimously rejected all three approaches because the offers significantly undervalued the company and its growth prospects.
The shares had been trading at about £31 a month ago before Takeda said in late March it was considering an offer for the Irish firm.
The two earlier cash-and share offers were worth 44 and 45.50 pounds per share respectively.
Bernstein analyst Wimal Kapadia said Shire was likely to be pushing for a larger cash component in current talks but Takeda was already stretched, suggesting the chances of a deal being consummated were still "reasonably risky".
Shire is best known for selling treatments for rare diseases and attention deficit disorder.