Details of his life at Chequers, the Prime Minister's country retreat in Buckinghamshire, is detailed in a biography titled 'Cameron: Practically a Conservative' to be published next week.
One "ally" of Cameron told the book's authors: "If there was an Olympic gold medal for 'chillaxing', the Prime Minister would win it."
"He is the model of how to have a clear divide between the world of work and then relaxation so you can clear your mind. There are very few people who have such a finely developed capacity to do that," Michael Gove, the Education Secretary and a family friend, added.
According to extracts published yesterday, Cameron is said to have been given the karaoke machine as a present from friends to mark the first Christmas since moving into 10 Downing street, the Daily Telegraph reported.
To escape the pressures of the problems currently gripping the country, he is also said to invite friends over for a game of snooker.
When he is on his own, he takes on a machine that fires tennis balls at him at high velocity, which he has nicknamed "the Clegger" following his closely-fought victory against the Deputy Prime Minister.
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The book is written by Francis Elliott of The Times and James Hanning of The Independent on Sunday.
Cameron, 45, has been dubbed "DVD Dave" for his love of box sets and mocked for enjoying weekly "date nights" with his wife, Samantha, 41.
The book claims the Prime Minister's Sunday routine generally starts early in the morning with the newspapers and time working on his computer.
Friends quoted in the book say that throughout the day it can then involve "a film on telly, play with the children, cook, have three or four glasses of wine with lunch, have an afternoon nap, play tennis".
The book also reveals how Cameron can be found surfing political betting websites.
With Britain in recession and the Conservatives slipping in the polls, the Prime Minister's leisure habits have increasingly been used as political ammunition against him by both Conservative and Labour opponents as a sign of a lack of application.