One thing he said the market has working against it is the growing unlikelihood that key tenets of President Donald Trump's pro-growth agenda will get enacted this year. Another is that productivity remains low, while a third is that economy is near full employment and rising wages could start pushing inflation higher.
However, Cooperman also said signs indicating that a market tumble is coming aren't in the air. The global economy is growing, the Fed and other central banks remain accommodative even though they are gradually tightening monetary policy, and there is a lack of "excesses" in pricing or sentiment.
If anything, he believes market structure rather than fundamentals could prove the biggest issue ahead.
"With all the technology and all these (exchange-traded funds) and quantitative systems that have been introduced, I do have concern that technology has outpaced the market's ability to handle it," Cooperman said. "When we get into the next bear market, it could be a messy affair."
He also is advising against bonds.
Investors have continued to pour money into fixed income despite signs that inflation is on the rise and yields are going to move higher as well. Rising yields come as prices fall, eating into the principal of fixed income instruments.
"At the moment, the bubble is not equities," Cooperman said. "The bubble is fixed income."