An agreement, which reports said could be announced later in the day, would put an end to an acrimonious war of words that has raged since Kraft launched a hostile takeover bid for Cadbury last year.
Bringing together top brands including Kraft's Dairylea cheese and Cadbury's Dairy Milk chocolate, a deal would also signal the iconic British firm had dropped determined efforts to fend off approaches from its US suitor.
The BBC reported Kraft may hike its offer to between 840 and 850 pence a share, saying that at 850 pence Cadbury would be valued at around 11.7 billion pounds (13.3 billion euros, or $19.1 billion).
This is significantly higher than the 10.5 billion pounds previously offered and is likely to be accepted by the Cadbury board, reports said.
The two firms were "highly likely" to agree a deal that would probably be jointly announced at 7am (0700 GMT) Tuesday, said the BBC's business editor Robert Peston.
A Cadbury spokeswoman declined to comment late Monday. Kraft could not be contacted.
Bankers for both companies were working through the night to finalise an agreement, The Times newspaper reported.
Midnight on Tuesday is the deadline for Kraft, the world's second-biggest snacks group after Nestle, to make its final offer.
Other leading brands that a tie-up would merge include Kraft's Kenco coffee and Toblerone and the British group's Cadbury Creme Eggs and Trident chewing gum.
If a deal is agreed by Cadbury's board, then the Kraft takeover would finally go through after months of hostility between the two firms.
Cadbury has put up a staunch defence against Kraft and insisted recently 2009 had been "outstanding", a claim dismissed by the US firm as "underwhelming."
The deal has faced opposition in Britain with protest from senior ministers over the attempt by a huge American firm to take over a homegrown company which traces its roots back to 1824.
"If you think that you can come here and make a fast buck you will find that you face huge opposition from the local population... and from the British government," Business Minister Peter Mandelson warned Kraft last month.
There have also been fears about job losses, with trade union Unite warning Kraft would be saddled with huge debts leading them to axe 7,000 posts at Cadbury and 20,000 at the company's sub-contractors.
US chocolate maker Hershey had also been considering a counter-offer for Cadbury, the Wall Street Journal reported Friday.
Hershey planned to bid at least $17.9 billion this week for Cadbury after concluding it can top Kraft's offer, the paper said.
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