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David Letterman may introduce his replacement to "Late Show" audience early. The veteran late-night talk show host will welcome his successor Stephen Colbert as a guest next week, on Tuesday, April 22.

This will be the first time the "Colbert Report" host visits "Late Show with David Letterman" since he was announced as the new "Late Show" host. He has been a frequent guest on the show.

Colbert will take over the CBS show after Letterman retires sometime in 2015. Fellow late-night show host Conan O'Brien has said that Colbert's the "right person" for the job. "I wasn't up for it," the comedian, who is currently hosting "CONAN" on TBS, said during a break from rehearsing for the recent MTV Movie Awards.

"I'm very happy where I am, but I love Stephen. I think Stephen is great. I'm a huge fan of his as a comic and as a human being. I think it's fantastic. I'm really glad that he got the job. I look forward to seeing his show." He added, "I was very happy because I have such respect for Dave. I'm glad that it's the right person getting it."