Just four months ago, Greenspan, who was the Fed chairman from 1987 to 2006, had said he thought prospects of the economy sliding back into recession and waned.
But Sunday on NBC's "Meet the Press," Greenspan cited the still-faltering housing industry as a sign it could happen.
Asked if a double-dip recession could occur if the housing crisis doesn't ease, Greenspan responded: "It is possible if home prices go down. "
He said while most economists "expect a small dip" in prices following the end of the home buyer's tax credit, "the data don't show that at this particular stage."
"If home prices stay stable, then I think we will skirt the worst of the housing problem," he said.
Still, another troubling matter is the potential for an increase in foreclosures, he said.
"Foreclosures would feed on the weakness in prices and it would create a problem so that it is touch and go," Greenspan said.
Greenspan said the country is in a pause in a modest recovery that "feels like a quasi-recession." It's possible the economy will get worse before it gets better, he said, "but not necessarily."
"Our problem basically is that we have a very distorted economy in the sense that there's been a significant recovery in a limited area of the economy amongst high income individuals who have just had $800 billion added to their 401(k)s and are spending it and are carrying what consumption there is," he said.
"Large banks who are doing much better and large corporations who you point out and everyone is pointing out are in excellent shape. The rest of the economy, small business, small banks, have a very significant amount of the labor force which is in tragic unemployment -- long-term unemployment -- that is pulling the economy apart."
Greenspan also said he doesn't see the unemployment rate improving any time soon.
In an April 4 appearance on ABC News' "This Week," Greenspan said he thought the odds of a double-dip recession "have fallen very significantly in the last two months," citing an improved stock market, rising capital investment, rebounding inventories, hope in the employment picture and the fading of the subprime mortgage crisis.