Billionaire investor Leon Cooperman told CNBC on Friday he's optimistic that the stock market has bottomed on coronavirus fears.

"If I'm right on the virus call, if I'm right and that's the big 'if' ... I think the market at the recent low ... was close enough to the bottom to be called the bottom," Cooperman said on "Squawk Box."

The S&P 500 hit its recent low of 2191.86 on Monday, which was about 35% lower than the index's last month's all-time high.

"If the economic shutdown goes beyond April into the third quarter, I would be less optimistic," said Cooperman, founder of the Omega Advisors investment firm, which he turned into a family office at the end of 2018.

The investor, who made his fortune picking individual stocks, said he sees an S&P range of 2,200 to 2,800 this year.

"I feel very strongly that individual stocks are much more attractive than [buying] the S&P 500," Cooperman continued. He said he has added to his Alphabet holdings in recent weeks.

"We're looking to add to Facebook and Adobe. We own Amazon. We look to add to that on weakness," he said.

Cooperman's comments Friday came as Dow futures were pointing to an opening loss of around 700 points.

The Dow Jones Industrial Average on Thursday surged over 1,350 points, or 6.4%, capping its biggest three-session winning streak since 1931. The S&P 500 rose 6.4% on Thursday.

Both indexes remained in bear market territory, with losses for each still exceeding 20% from recent 52-week highs heading into Friday's trading.

"I found the rally off the bottom in the few couple days impressive. I think it's gone as far as it should go," Cooperman said. "The market is in the zone of fair valuation. Until we get more of a handle on the virus, I would think that one should be very defensive."

Earlier this month, he said investors who are trying to manage the stock market's coronavirus-driven volatility needed to be patient. Don't buy on margin, "just know what you own and be patient," Cooperman told CNBC on March 1.

Cooperman offered similar advice Friday, telling investors "that this is not your last chance" to buy.

"I would not want to borrow money. I would want to be a cash-basis investor. I would want to stick with quality in the market," he said.