The two firms could make an announcement in the morning
Kraft Foods is expected to raise its bid for Cadbury to a level that is accepted by the UK firm, BBC business editor Robert Peston has learned.
He says the US giant may raise its offer to between 840 and 850 pence per share, with 850p valuing the chocolate-maker at £11.7bn.
Kraft launched its hostile takeover bid for Cadbury in December, having its previous offer of 761p rejected.
The two firms may jointly announce the successful bid later.
Shares in Cadbury ended Monday trading up 14 pence or 1.8% to 807.50p.
No-one from either Cadbury or Kraft has been available for comment.
Our business editor said it now seems "highly likely" that Kraft and Cadbury will agree a deal that will probably be announced at 0700 GMT.
John Cadbury, a Quaker, opened a shop in Birmingham in 1824, selling tea, coffee and hot chocolate - as an alternative to alcohol
Dairy Milk brand introduced in 1905, with Milk Tray coming 10 years later
Merged with Schweppes drinks business in 1969. Its drinks arm was spun off in 2008
Employs about 45,000 people in 60 countries
An agreement between the two companies would end the intense animosity between the firms that first manifested itself when Kraft announced its desire to own Cadbury last autumn.
It would also end any doubt at all that Cadbury will lose its independence.
There would still be a theoretical possibility that the US confectioner Hershey would come in with a higher offer.
But if Cadbury's board recommends Kraft's bid, it means that the company will be taken over.
Negotiations between Cadbury's bankers and Kraft's bankers are taking place overnight.
Founded in Illinois as a cheese wholesaler in 1903
Bought in 1988 by Philip Morris, which also purchased Nabisco for $19.2bn in 2000 before integrating it into Kraft Foods
More than 40 of its brands are more than 100 years old
Has 98,000 employees and 168 manufacturing and processing facilities worldwide
Unions and analysts have both warned that there will likely be job losses among Cadbury's 45,000 workforce following a takeover.
Kraft has a Tuesday deadline to make its second and final formal bid for Cadbury, or else have to walk away from the deal for a year.
The US giant had previously faced pressure from its leading shareholder - US billionaire investor Warren Buffett - not to overpay for Cadbury.
However, Kraft raised extra funds earlier this month when it sold its North American pizza business to Swiss group Nestle for $3.7bn (£2.3bn).