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Macy's CEO on sale rumors: Company will do 'the right thing for our shareholders'

Macy's CEO Terry Lundgren told CNBC on Tuesday that the company will do the right thing for its shareholders amid rumors it could be seeking a buyer.

"You've heard and talked about the rumors of somebody buying us, and you probably also heard we're buying them," Lundgren said on "Squawk Box."

"We're not going to be a highly leveraged retailer because those movies never turn out well. We've seen that before," he said.

Earlier this month, the New York Post reported that Lundgren, expected to step down later this year, was open to offers in an attempt to avoid a board shake-up that could tarnish his legacy.

Sources told the newspaper that Jeffrey Smith's Starboard Value, an activist New York hedge fund, is fed up with Macy's performance. Smith invested in the company in 2015. Starboard is prepared to mount a proxy battle for board seats, the sources said in the report.

Lundgren's comments on Tuesday also came after the department store chain posted earnings that beat expectations, but its top line fell short.

The CEO said Tuesday that there will be plenty of traffic in malls across the U.S. even as more consumers shift to online shopping.

"They're going to fewer stores because they're using their mobile device to decide. Instead of just wandering and going to five, six, seven locations, they know where they're going to go," he said.

He continued: "There probably will be some more consolidation. We've initiated that in our own company. We think we're in a good position at this point."