That will lave little room for growth both in economic measures and in most investment classes, Roubini said.

"There is that risk because the problems on the macro level are first in the euro zone. Then in China there is evidence of economic slowdown...Japan is in trouble and US economic growth is going to slow down," he said. "There is also regulatory risk because we don't know how financial reform is going to occur."

Investors then should focus on buying debt from countries that are solid economically.

"Apart from cash I would invest in short-term government bonds of countries that don't have a serious debt problem, countries like Germany and maybe Canada, a few other advanced economies that from a fiscal point of view are sounder than the weaker economies," he said.

As for Europe, he called fixing the debt problems in Greece and other troubled nations "mission impossible" and said tough decisions will need to be made.

"What needs to be done is clear. We need to raise taxes and cut spending. Otherwise we're going to get a fiscal train wreck," he said. "It's going to take years of sacrifices."

In 2006 Roubini predicted the impending housing bust and ensuing financial crisis. His predictions and comments are widely followed in financial circles.