Young people are flocking to the city, as suburban living becomes less appealing, real estate mogul Sam Zell told CNBC.

However, all the growth impacting cities has a distinct downside:

One of the byproducts of people moving to cities is soaring demand for apartments. "We are seeing 96 percent occupancy," said Zell—who's chairman of the real estate investment trust Equity Residential, one of the largest apartment groups in the country. Of the 18,000 units the REIT manages in New York City, Zell estimated 45 percent are occupied by just one person.

"It's probably going to happen here in New York first," he said. "You're going to see 300-square-foot apartments, directly related to that one person wanting to live alone—and saying, 'I'll give up space for privacy.'"