06/15/2012 08:08 am ET Updated Jun 15, 2012

Regis Philbin Tries To Convince David Letterman To Do A Weekly TV Show With Him (VIDEO)

Regis Philbin may be just about the hardest-working retiree in show business right now.

He stopped by "Late Show" (Weeknights, 11:35 p.m. ET on CBS) Thursday night and pitched his idea for a new show to his old pal David Letterman.

Building on the popularity of their stint on on "Piers Morgan Tonight" on CNN in May 2012, Philbin suggested they do their own TV show.

"A weekly show. Once a week." he said. "We'll do that," agreed Dave.

But when Reege elaborated -- "Dave, on the way home, stops by ... " -- Letterman got cold feet: "No, no, no" he said.

Undeterred, Philbin carried on: "and we shoot the breeze together."

Letterman advised Philbin to instead accept NBC's offer of filling-in for Hoda Kotb on "Today" with his old sparring partner, Kathie Lee Gifford.

Ever the trouper, Philbin was game even though he claimed he didn't know who Hoda is.

"Late Show With David Letterman" airs weeknights, 11:35 p.m. ET on CBS.

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