Today, his audience is a little harder to please. In fact, a mere mention is met with a deafening snore.
"Sorry, sometimes I fall asleep when he starts talking about himself a lot, which is all the time," explains Constantine, Gervais's minuscule co-star.
The frog, who could be Kermit's double (a dark mole above his mouth being the only thing that distinguishes the two) plays the 'World's Number One Criminal' in new movie Muppets Most Wanted.
Perhaps Constantine, who speaks with a thick Russian accent, has heard of Extras, another of Gervais's TV hits?
"Is that like when you need a newspaper? Extra, extra?" asks the Muppet, who is dressed in a T-shirt that reads 'I'm Not Kermit'.
This blase approach to Gervais' career may be unusual given the comedian and writer's numerous Bafta wins, Golden Globe presenting slots and Hollywood hits, but it's clear from the regular peals of high-pitched laughter that erupt from the 52-year-old Brit that he's having a blast next to his felt friend.
A lifelong Muppets fan, Gervais, who used to watch the popular series in the Seventies with his older siblings, was thrilled to land the role as the "lead human" in the new film, which sees the entire Muppets gang, including Kermit and Miss Piggy, heading to Europe for a much touted tour.
"I've been a fan of the Muppets for many years, but this is my first time acting opposite a frog. It's probably the best experience of my life.
"This is a big Hollywood production. The sets are amazing, the effects are great, it's a really funny caper plot," explains the star, who recently announced that he has plans to film a mockumentary series following his Office character David Brent as he tours with his band, Foregone Conclusion.
There is plenty of adventure for the Muppets, as they go overseas and find themselves unwittingly entangled in an international crime caper headed by baddie Constantine and his dastardly sidekick Dominic Badguy ("Badgeee, it's French"), played by Gervais, who also acts as the Muppets' tour manager.
Gervais isn't the only human making an appearance in the movie. There's also Modern Family's Ty Burrell, who plays French officer Jean Pierre Napoleon, Tina Fey as Nadya, a Russian prison guard who has a soft spot for Kermit, and a constant stream of cameos, from Mackenzie Crook to Salma Hayek, Chloe Grace Moretz, Tom Hiddleston, Stanley Tucci and Miranda Richardson.
Fans of The Office might recall Gervais's wince-inducing dance in an episode of the early Noughties series, but the idea of dusting off his dancing shoes again for Muppets Most Wanted wasn't a welcome one.
"I found the dancing a bit awkward," explains Gervais, who also sings in the film. "I'm not a great dancer but Constantine's a great dancer. His little flippers can go nine to the dozen."
"Nineteen to the dozen," corrects his puppet friend.
Gervais reveals he had a very small part in The Muppets blockbuster in 2011.
The scene was eventually cut, with the director James Bobin explaining, "It wasn't right for the movie", but the film-maker knew that Gervais would be a "fantastic" fit for his next movie.
"But this time do you know what he is?" adds the frog, leaning forwards. "He is big star of the movie. He up on poster, his name is on poster."
Gervais collapses into another round of the titters. "Sometimes interviews are a bit awkward," he says, catching his breath.
"They're not much fun, but with an evil Russian frog, everything's all right."
"The Office was good, Extras was good, Golden Globes was good," he notes."But this is it, talking to an evil Russian frog in a little T-shirt."