Harris, who is currently starring in Hedwig and the Angry Inch on Broadway, said he was approached about doing a late-night show before David Letterman announced his retirement.

"I felt like I knew what my skill set was and what I wanted to do after ['How I Met Your Mother'], with them," Harris said on Howard Stern's radio show. "It surprised me [CBS' Les Moonves] pitched me that idea. I sat for a time with it while I was talking to him, and I told him what concerned me about the longevity of that kind of gig. I think I would get bored of the repetition fast. The structure is so set — I don't have any interest in doing Monologue, Commercial, Sketch, Guest, Guest, Musical Act, Good Night."

Instead, Harris said he would like to host a weekly variety show for CBS. Stern asked if Moonves was interested, and Harris said, "Yeah — he still might be."

Harris received a Tony Award nomination for his performance in Hedwig and the Angry Inch. He starred as Barney Stinson in the hit sitcom "How I Met Your Mother" for nine seasons and has performed on Broadway in Assassins and in the New York Philharmonic production of Company.

Harris has been honored with four Emmy Awards: three for his acclaimed hosting of the Tony Awards and another for his guest-starring role on "Glee." He also served as host and producer of the 61st and 65th Primetime Emmy Awards.