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Drugmakers AbbVie and Shire are in detailed talks about a possible combination after AbbVie once again raised the deal price and gave Shire shareholders a bigger stake in the new company.

Shire says North Chicago, Illinois-based AbbVie is now offering a cash-stock combination valued at 53.20 British pounds ($91.10) for each share of Shire, which is headquartered on the British island of Jersey.

The new offer totals roughly $53.68 billion and represents an increase from AbbVie's previous proposal, which amounted to around $51.3 billion pounds.

Shire Plc shareholders also would own about 25 percent of the combined new company, up from the 24 percent stake proposed in the most recent offer.

Shire had rejected three unsolicited offers from AbbVie Inc. before asking for a revised proposal earlier this month.