Enzo Maccarinelli has called David Haye "delusional" ahead of their cruiserweight unification fight at London's O2 Arena on 9 March.
London's Haye, 27, the WBC and WBA title-holder, said he can beat Swansea's Maccarinelli, who holds the WBO belt, inside a minute of round one.
Haye also claimed he has fought at a higher level than Maccarinelli, 27.
"He can say what he likes but he's delusional. I'll punch a hole in his head," Maccarinelli told BBC Sport.
Maccarinelli has won 28 of his 29 paid fights, including 21 knockouts, while Haye has 20 wins from 21 fights, including 19 inside the distance.
Given these statistics, many expect the clash, which will take place in the early hours of the Sunday for the benefit of an American audience, to be the most explosive domestic match-up since Nigel Benn-Chris Eubank II in 1993.