Andre Ward wants Sergey Kovalev to know he's in for a bad night when they face off in the ring again ... telling TMZ Sports "he's got big problems" come June.

The Champ says he's not fazed by Kovalev threatening to end his career  ... and even challenges the Krusher to back up his words.

Ward says Kovalev's words only fuel his drive to dominate the light heavyweight rematch ... and hints there won't be any controversial decision this time around.

June 17 can't come soon enough.