Private equity group Kohlberg Kravis Roberts (KKR) has upped its offer for pharmacy group Alliance Boots (AB) by 40p per share.
Stefano Pessina, the deputy chairman of Alliance boots, is heading the deal which sees the firm valued at £10.2 billion or 1,040p per share.
"The board has agreed to grant KKR and Stefano Pessina a limited period to undertake confirmatory due diligence," a statement from the group said.
An earlier offer from KKR and Mr Pessina of 1,000p per share was seen to be too low for the group but the increased offer has allowed the suitors to inspect the books of the firm.
"A further announcement will be made as and when appropriate," Alliance Boots added.
Earlier this week a trading update from the group revealed that full year results were expected to be in line with predictions while fourth quarter underlying revenue growth in the UK was reported to have increased by 2.3 per cent.
Insider reports of a second offer from UK investment Terra Firma have also been circulating.
AB was created through a £7 billion merger just nine months ago.