KKR and Pessina raised their offer 50p above their initial£10.40-a-share approach.
Pessina, who is Boots' biggest shareholder with a 15 per cent stake, would invest up to£1 billion of his own money in what would be Europe's largest private equity buy-out.
Analysts believe the deal with KKR and Pessina - the Italian businessman who created Alliance Boots through the merger of his wholesale company Alliance UniChem with the high street chain - is likely to go through.
KKR partner Dominic Murphy said: 'Our objective is to work with Stefano Pessina and the existing management team to enhance Alliance Boots' position as a global leader in the healthcare services and beauty industries. KKR is committed to building on Alliance Boots' unique position as a trusted UK brand and retail institution and further developing the group's existing businesses, both in the UK and overseas.'
Pessina said: 'The markets we serve are changing dynamically. We are committed to accelerating the development of Alliance Boots in order to meet the challenges and opportunities we face.'
However, Terra Firma - Guy Hands' private equity firm - and medical charity Wellcome Trust revealed HBoS has joined their rival bid for the pharmacy chain. The consortium made an offer of£10.85 a share in cash and is waiting for a response from the board.
Alliance Boots also revealed its UK wholesale business Unichem has entered into an agreement with AstraZeneca to act as its agency partner to deliver prescription medicines directly to pharamacies, doctors and hospitals across the UK. The supply arrangements will be implemented later this year.
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