If Letterman is able to reach an agreement with CBS, he will become the longest-running late-night host in US television history with 32 years on the air, surpassing his mentor Johnny Carson. His current contract ends in August.
Sources close to the negotiations have told The New York Times that CBS is currently in talks with Letterman's staff for contract extensions, which could incidate that a deal with the presenter himself is nearly complete.
The effect that Letterman's possible contract extension could have on Late Late Show host Craig Ferguson is not yet known. Ferguson is contractually guaranteed to replace Letterman on CBS when he eventually retires.
Letterman debuted in late-night for NBC in 1982, but left the Peacock Network 11 years later when he was not chosen to replace Johnny Carson as host of The Tonight Show.
The Late Show with David Letterman airs weeknights at 11.35/10.35c on CBS.
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Watch a clip from David Letterman's first NBC Late Night show below: