Investors in the British confectionary company have been holding out for a higher offer, and Kraft now wants an extension on the deadline for its current cash-and-shares bid.
The offer was due to expire tomorrow, but Kraft will ask the Takeover Panel for more time to come up with a better proposal.
Shares in Cadbury closed at 797p at the end of December 61p higher than Kraft's current offer, leaving the US food giant little choice but to increase its bid if it wants to win shareholders round.
The US company has until 19 January to table an improved bid. After that, it can only make a higher offer if a rival suitor comes forward.
One of those considering a potential counter bid is Hershey, the American chocolate maker, which has been working on an offer for several weeks. Nestle and Ferrero Group of Italy are also mulling rival offers.
Key to all interested parties is Cadbury's latest trading information. An update is due on 15 January.
Cadbury chairman Roger Carr denounced the existing Kraft offer as "derisory" and an attempt to "steal the company on the cheap".
The board has promised shareholders better growth prospects as a standalone company, saying a tie-up with Kraft would condemn Cadbury to a lacklustre future.
But the board would come under pressure to open Cadbury's books if a bid of more than 800p a share was put forward. Unless a rival bidder emerges, Kraft must win the support of more than half of the shareholder register by 2 February or walk away.