If a Sears store near you has already closed or is in the process of closing, it's likely the owner of that property will opt to demolish it rather than find someone to fill the space.

The bankrupt department store chain has already said it will shut 142 stores by year's end. And its future while it's in bankruptcy court proceedings is still uncertain, with a total liquidation being one potential outcome. That would mean more than 500 additional Sears and Kmart stores going dark.

As mall owners look to find new tenants to replace Sears, the process likely won't be so easy. Sears stores are typically more than 100,000 square feet and can occupy multiple levels. There are few department store chains — or any retailers — still growing today that would fit directly into that space. Some, if not lots, of construction is going to be required.

To be sure, a handful of companies have already expressed interest in taking over Sears' real estate that's currently being bid on, and moving right in. The short list includes furniture retailer At Home, self-storage company U-Haul and off-price chain Burlington.

"We are looking at both Sears and Kmart stores that have a large enough floor plan to accommodate our square footage," a spokeswoman for At Home told CNBC. "We have actually been scouting those for about four years as they become available on the market."

Court documents filed in Sears' bankruptcy case show U-Haul hopes to take 13 locations from Sears for $62 million, including 12 Kmart stores. Real estate analysts tell CNBC there's still a huge demand in the U.S. for self-storage facilities, and more of these types of companies are likely to be interested in Sears' real estate.

Burlington CEO Tom Kingsbury, meanwhile, told investors last month "Kmart is more of an opportunity" for the company "because they're in very good locations." But, he added, "we have taken advantage of some of the Sears closures, where we'll take a piece of the building and somebody else would take another piece of the building, and they'll divide it up."