Citing sources close to Stern, the newspaper said the shock jock is "being groomed" to replace Fallon, who is reported to be in line to replace Jay Leno on "Tonight" when Leno's contract expires in 2014.
Stern has his own satellite radio show and is a judge on "America's Got Talent."
His agent, Don Buchwald, declined to comment in the report, as did NBC's late night programming chief Doug Vaughan, the Post said Wednesday.
Millions of Getty images now available for free via embed tool
Boston schools pull out free condoms over wrapping complaints