The couple announced their plans to get married just five months ago, but according to Life & Style magazine, Jesse has told his inner circle that it's all off.
'That's what he's telling pals,' said an insider. 'He says there's too much drama for him.'
And recent posts of Twitter by the pair have also fuelled speculation that all is not well.
Earlier this month Jesse Tweeted, 'I guess I was trying to take too much from the world. Funny how things go from amazing to s--t in the blink of an eye,' while Kat wrote, 'I have no regrets,' later that day.
They have not been seen together side by side since Jesse's book-signing event in LA on May 14.
The couple first got together in August 2010, less than two months after Jesse and Sandra Bullock divorced amid allegations that he had been unfaithful.