The newspaper printing presses may have another decade of life in them, New York Times CEO Mark Thompson told CNBC on Monday.

"I believe at least 10 years is what we can see in the U.S. for our print products," Thompson said on "Power Lunch." He said he'd like to have the print edition "survive and thrive as long as it can," but admitted it might face an expiration date.

"We'll decide that simply on the economics," he said. "There may come a point when the economics of [the print paper] no longer make sense for us."

"The key thing for us is that we're pivoting," Thompson said. "Our plan is to go on serving our loyal print subscribers as long as we can. But meanwhile to build up the digital business, so that we have a successful growing company and a successful news operation long after print is gone."

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Digital subscriptions, in fact, may be what's keeping the New York Times afloat for a new generation of readers. While Thompson said the number of print subscribers is relatively constant, "with a little bit of a decline every time," the company said last week that it added 157,000 digital subscribers in the fourth quarter of 2017. The majority were new subscribers, but that number also included cooking and crossword subscriptions.

Revenue from digital subscriptions increased more than 51 percent in the quarter compared with a year earlier. Overall subscription revenue increased 19.2 percent.

Meanwhile, the company's fourth-quarter earnings and revenue beat analysts expectations, "even though the print side of the business is still somewhat challenged," Thompson said. Total revenue rose 10 percent from a year earlier to $484.1 million. New York Times' shares have risen more than 20 percent this year.

Even with the recent market volatility the stock is up 8 percent from last week.

Under Thompson's leadership, the New York Times has become the first news organization in the world to pass the 1 million digital-only subscription mark.

"Without question we make more money on a print subscriber," Thompson said. "But the point about digital is that we believe we can grow many, many more of them. We've already got more digital than print subscribers. Digital is growing very rapidly. Ultimately, there will be many times the number of digital subscribers compared to print."