Greenspan also said in an interview on CNN's "Late Edition with Wolf Blitzer" that the turmoil caused by the subprime mortgage crisis was easing and financial markets were beginning to go back to normal.
Greenspan said Americans should be "cautious" about the economy, but not necessarily nervous.
"I think the best way of putting it is that the American economy's rate of growth is definitely slowing down," Greenspan said, adding that the odds of a recession are less than 50/50.
Greenspan added that he thought there was not much that lawmakers and the Federal Reserve should be doing to avoid a downturn.
"I doubt very much if there is anything that can or should be done. Because remember, we have a very complex, self-calibrating, self-adjusting economy," he said.
Greenspan, who left the Fed in January 2006, has been making extensive public appearances to promote his memoir, "The Age of Turbulence," which was published last month.
The U.S. economy grew at a relatively brisk 3.8 percent annual rate in the second quarter, but is forecast to slow significantly during the third quarter because of a continuing slowdown in the housing sector.
Greenspan said dealing with the overhand in the U.S. housing market quickly will help get the economy back on track.