David Simon, chairman and chief executive officer of Simon Property Group Inc., speaks during the Milken Institute Global Conference in Beverly Hills, California, April 30, 2018. Dania Maxwell | Bloomberg | Getty Images

The biggest mall owner in the U.S. is warning of more store closures and even bankruptcies to rattle the retail industry in 2019. "There are some retailers out there that we're nervous about," Simon Property Group CEO David Simon said Friday during a call with analysts after the company reported earnings, though he didn't name those companies. "We are concerned about a few [retail bankruptcies] that should shake out in the first quarter."

Simon, the largest mall owner in the U.S., has like its peers been grappling with how to deal with an onslaught of store closures from tenants big and small, ranging from Sears to Starbucks' Teavana. The real estate investment trust finds itself in an especially unique position with Sears' bankruptcy in that it's also a member of an unsecured creditors committee now arguing Sears can't be saved, as Sears Chairman Eddie Lampert is still trying to salvage some 400 stores. David Simon had said last October, right after Sears filed for Chapter 11 bankruptcy protection, that he had put the department store chain "in the rearview mirror." He called the whole situation "tragic" but said hotels, office spaces and gyms would move into malls and fill gaps left behind by Sears, J.C. Penney and others. The topic of Sears' fate specifically didn't come up on Friday's conference call, other than Simon saying the company was on its 200th unsecured creditors committee with Sears, now. When asked if Simon had been in talks with department store operator J.C. Penney, which is expected to announce additional store closures at the end of this month, Simon said, "no." Most of the retailers struggling today and expected to shut more stores are highly levered, according to Simon. "We have a long list of retailers that have struggled. ... And 80 to 90 percent of that list have been over-levered so they couldn't turn left or right."