MSNBC is reporting it this afternoon:
In an interview with the Cleveland Plain Dealer, the congressman said he was quitting the race and would made a formal announcement Friday.
"I want to continue to serve in Congress," he told the newspaper.
Kucinich said he will not endorse another Democrat in the primary.
The Cleveland-area congressman is facing a challenge to his seat in the House from Joe Cimperman, who has begun running an attack ad accusing Kucinich of being a "part-time congressman" and missing more than 300 votes in the House.