US-based private equity group Kohlberg Kravis Roberts (KKR) has improved its bid approach for UK chemist and drugs wholesaler Alliance Boots to £10.2bn.
KKR had been expected to come back with a higher offer.
The new £10.40 pence-a-share proposed offer is 40p more than an earlier approach, which Boots rejected.
The move has the backing of Italian billionaire Stephano Pessina - who controls a 15% stake in Boots.
Boots has agreed to open its books to KKR and news of the higher offer pushed the chemist chain's shares higher.
Boots shares closed 0.5 pence lower on the London market, at 1026.5p after earlier climbing as high as £10.40.
BBC business editor Robert Peston said that Boots was likely to recommend its shareholders accept a bid at that level and that the firm was "on its way into new ownership".
He said that it was "highly unlikely" that a formal bid from KKR would not now materialise.
"The only question now is whether Boots will end up being owned by KKR/Pessina or whether another bidder or bidders (which would also be from private equity) now emerges," he said.
Last weekend, reports linked UK investment group Terra Firma with a move for Boots.
Retail analyst Richard Ratner of Seymour Pierce said that the Alliance Boots board had "saved face" by pushing the price higher.
"Of course, somebody else might appear, but Mr Pessina is key to the wholesale business so the odds must be on his offer going through," Mr Ratner said.
Alliance Boots is best known in the UK for its 2,600 Boots the Chemist shops on the High Street.
But since its £7bn tie-up with Alliance UniChem last year it is now also a major drugs wholesaler, with a 40% market share, supplying more than 125,000 pharmacies, health centres and hospitals.
Mr Pessina is believed to want to take the company private and grow it away from the public spotlight.
But trade unions have warned that selling the group to a private equity firm could lead to asset-stripping.
Earlier this week Boots unveiled plans to rebrand its UK pharmacies, and said it was is cutting 300 manufacturing jobs at its Nottingham factory after losing a contract with Reckitt Benckiser.