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Japan's Takeda Pharmaceutical is in talks with Shire after making a £43bn bid for the London-listed rare diseases drug maker.

Shire's board rejected the cash and stock offer of £46.50 a share that was made on 12 April.

However, Takeda said that discussions between the two firms about a potential offer were continuing.

with Takeda to determine if it could make a higher offer.

However, the prospect of a bidding war for Shire receded after Botox maker Allergan, which had said it was considering a takeover offer, said it was not going to make a bid.

Shire said that Takeda had made three approaches, with the first worth £41bn on 29 March.

The most recent offer was worth £43bn and would result in Shire shareholders owning about half the enlarged group.

That offer was rejected by Shire's board as directors said it "significantly undervalued the company, its growth prospects and pipeline".

Shares in Shire closed on Thursday £2.21 higher at £39.75. 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.

Takeda said it would only make a firm offer with the backing of Shire's board and following satisfactory due diligence.

The Japanese firm is interested in a Shire takeover to strengthen its cancer, stomach and brain drug portfolio.

This week Shire said it was selling its cancer treatment unit to France's Servier for £1.7bn in a deal that was initiated in December and was unrelated to the possibility of a takeover bid.

Shire was founded in the UK and still has a large base in Basingstoke, but moved its corporate headquarters to Dublin a decade ago. It has 24,000 employees in 65 countries.

According to the company, there are 7,000 rare diseases, but fewer than 5% have a treatment. Most are genetic and about half begin in childhood.