The latest proposal - the fifth one made by Takeda - comprises GBP27.26 in new Takeda shares and GBP21.75 in cash for each Shire ordinary share. That rings up at 0.839 new Takeda shares and $30.33 for each Shire share - or close to $65 billion, with Takeda tacking on about $2.5 billion.
"On this basis the revised proposal is equivalent to a value of approximately £46 billion for the entire issued and to be issued share capital of the company", the Irish company said. Accordingly, the Board will engage in discussions with Takeda in relation to these terms.
"They have a lot of treatments for rare diseases, where the barriers to entry for other companies are very high".
Shire PLC (NASDAQ:SHPG) traded down 0.52% during midday trading on Monday, hitting $164.17.
If successful, it would be the largest overseas acquisition by a Japanese company and propel Takeda, led by Frenchman Christophe Weber, into the top ranks of global drugmakers.
Takeda added in its own statement that it meant to maintain its dividend policy and investment-grade credit rating following the deal.
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But he said Shire offered an attractive portfolio. The company has market cap of $48.58 billion. It said on Wednesday it meant to maintain its dividend policy and investment-grade credit rating following the deal. Representatives for Takeda and Shire declined to comment.
Shire has always been seen as a likely takeover target.
Botox maker Allergan confirmed last week it would not make a bid for Shire, just a day after saying it was weighing up an offer.
This isn't the first M&A bid for Shire - a $52 billion takeover by AbbVie had been agreed but was terminated in 2014 because of a change in United States tax rules. Shire also has a track record of acquisitions, but its biggest ever deal - the $32 billion purchase of Baxalta in 2016 - was widely criticized by shareholders.
Shire traces its roots back to 1986, when it began as a seller of calcium supplements to treat osteoporosis, operating from an office above a shop in Hampshire, southern England.
Acquiring Shire would vault Takeda, which has few late-stage experimental drugs in its pipeline, into the ranks of the world's top pharmaceutical companies.
Earlier this month, Shire entered into a deal to offload its oncology business to France-based Servier for $2.4bn.