The man, whose name was not released, was inside Macy's about two days ago when he allegedly made the comment, according to The Desert Sun.
"You can't just walk in somewhere and say something like that," Valenzuela told the newspaper.
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Security personnel at Macy's spotted the man back inside the store on Sunday, and though he did not make any threats at that time, they notified authorities, the newspaper said.
Valenzuela said the Macy's security team was concerned for the public's safety, The Desert Sun reported.
Two men who allegedly pulled guns and shot at each other at the Palm Desert Toys "R" Us store on Nov. 28 died in that confrontation.
Dennis Gutierrez of the Riverside County Sheriff's Department said Monday he could not give any details about the alleged threat.