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3. Craig Ferguson

The Scot's Late Late Show follows Letterman at 12.30am, and is produced by Letterman's company, Worldwide Pants. It's also been reported that Ferguson has a clause in his contract making him first in line once Dave retires. Yet he's never shown much enthusiasm for the job, declaring in 2009 that "there's a world of pain that comes with 11:30 that doesn't exist at 12:30". And speculation is rife that he has no plans to renew his contract in 2014, leading CBS to possibly turn to another Brit ...

4. John Oliver

Oliver's star has risen considerably since he provided holiday cover for former boss Jon Stewart as host of The Daily Show. He'll soon have his own "fake news" show on HBO, Last Week Tonight with John Oliver, and has reportedly been approached about taking over Craig Ferguson's show. Is it too much of a stretch to imagine that he'll be considered for the big job? Whatever the case, the very thought of a Birmingham-bred former Footlights member even coming close to hosting a US TV institution is funnier than any Jay Leno routine.

5. Paul F Tompkins

He's far from a household name, but this nattily attired stand-up is easily one of the most likeable and effortlessly funny men in US comedy today. Not only is Tompkins a superstar in the ever-booming world of comedy podcasts, he's one of the best improvisers around, he does sketches and characters (his Werner Herzog and Garry Marshall impressions are a source of never-ending joy for listeners of Comedy Bang Bang), and on his Speakeasy YouTube channel he's proved to be a warm and personable celebrity interviewer. Realistically, he's unlikely to be on CBS's list – but he should be.

6. Jon Stewart

The host of The Daily Show, however, has to be near the top of that list. Stewart is used to the daily grind of a talk show, and has a loyal young audience who would no doubt follow him to the older-skewing CBS. There's just one problem. With a reported salary of $30 million, Stewart is the highest paid host on US TV – if he were to take Letterman's job he might need to take a pay cut.

7. Chris Rock

He's razor-sharp, professional yet crazy enough to keep things interesting, and gets on well with Letterman (who will surely have a hand in choosing his replacement). Rock also got the job in Louis CK's fictionalised version of the battle for the Late Show. The fact that Rock is black is almost by the by – he'd be a very safe choice. But he's done this job before, for HBO, and appears to enjoy packing out arenas on his stand-up tour and dabbling in movies. Would he really want to swap that for the chance to chat to, say, Kate Bosworth about her new film?

8. Chelsea Handler

For no other reason that she recently announced a plan to leave her low-rated E! show Chelsea Lately, Handler has inexplicably become the bookies' pick for "first female host of a late night network talk show". But despite her manager's assertion that "We have at least seven suitors and many ideas", it seems unlikely that the Letterman job will be one of them. Not because she's a woman, but because her lemon-sucking screen persona is even more prickly than Letterman's, there's scant evidence that viewers like her, her booze-addled party girl persona seems like an odd fit with CBS, and – crucially – she just isn't very funny.

9. Tina Fey

She helped make the Golden Globes watchable; she makes anything she's in instantly funnier; even people who've never seen 30 Rock find her adorable. What sane person wouldn't want an hour of Tina Fey on TV every weeknight? Tina Fey, for one. Fey's brand of good-natured snark would undoubtedly be a breath of fresh air in late night television's stuffy green room, but she called an end to 30 Rock so she could see her family more. She'd see even less of them if she got this job.

10. Ricky Gervais

Don't laugh. Despite the strong reactions he tends to provoke at home in Britain, Gervais is approaching comedy royalty in the US. He's friends with, and respected by, many others on this list (Seinfeld, CK, Rock, Fey) and is already a regular fixture on the US talk show circuit, having appeared on the Late Show couch alone 25 times so far. (In a farewell tweet made after Letterman's announcement, Gervais described the host as "probably the man most to blame for inflicting me on America". ) Could he make the leap to the other side of the desk? Stranger things have happened; his three-times hosting of the Golden Globes, for example.

READ: Jay Leno: Good night, and good riddance