Cronkite, 89, lives in the same building as Simon, 65, the New York Post reported Wednesday.
Cronkite's wife of 65 years died from cancer in March.
"My wife has only been gone less than a year. I'll wait until that year has passed, at least," he said. "We are keeping company, as the old phrase used to be. I'm not making any moves immediately. I don't think it's proper."
Simon's husband, former New York Times Magazine articles editor and author Gerald Walker, died from complications of a stroke in early 2004.
Simon -- an opera singer -- won an Emmy Award as arts correspondent with PBS' "McNeil-Lehrer News Hour" from 1986-1992.
Notable deaths of 2014 [PHOTOS]