"We just received poll results this week," a campaign official said. "It was clear Bruce could not close the gap."
Douglas, who had vowed to spend millions of his own dollars, had made education reform the centerpiece of his campaign. However, during recent appearances with Fisher, Douglas had fared poorly and that was apparently reflected in the poll results.
The campaign aide said Douglas was told the only way he might gain ground on Fisher was "to beat him up, to really go negative. He didn't want to do that."
Douglas' decision leaves Fisher to face Republican Bob Taft in November. Taft is unopposed in the GOP primary.
Campaign sources said Douglas, who had hired some of the most talented political consultants in the Democratic Party, had spent more than $1 million so far.
Fisher, who was campaigning Wednesday in Dayton, said, "I've heard the rumors, but they haven't been substantiated enough for me to comment."
Douglas, 64, made a fortune in the construction business in Toledo before going to Harvard to study public policy and then, in 1995, creating The New Ohio Institute, a think tank that focused on urban issues, primarily education.
Douglas called for a 1 1/2 -cent increase in the state sales tax for education and property tax relief, arguing that a proposed 1-cent increase contained in State Issue 2 was insufficient.