It follows media speculation that the Scottish Secretary could be a potential successor to Nick Clegg.
Opinion polls have suggested the Lib Dems are set to lose many seats across the UK and Scotland in May's general election.
Mr Carmichael's Orkney and Shetland seat is considered to be one of the party's safest.
This has led to him being named in some quarters as a possible future leadership contender.
But when asked whether he would like to lead the party, Mr Carmichael said: "No. There's no vacancy and I have the constituency that is furthest away from London.
"I have got a family that still includes school age children. And the commitment that it takes to be party leader in modern politics is enormous.
"My family already miss out on a lot just by virtue of the fact that I'm an MP and I'm a minister and I'm away from home every week .
"At least I feel that they miss out on a lot, they might feel differently."
Mr Carmichael did not rule out continuing to have a role at the Scotland Office if the Lib Dems were in coalition after May.
He said: "Who has a job anywhere is for the prime minister and deputy prime minister, and that is well above my pay grade. I have loved every second of being a minister but I've loved every second of being an MP."

Soldiers from both sides shared an impromptu ceasefire in Ypres, Belgium, on Christmas Day 1914.
Graham Brookland of the Army FA said the match would "commemorate the occasion in an extremely good spirit".
The game, played at Aldershot Town FC in Hampshire, ended in a 1-0 win for the British Army.
Several thousand events have been held across the UK to mark the Christmas truce football match as part of Football Remembers Week.
Every team in the Premier League and Football League have marked the centenary of World War One at recent matches.
The famous "Christmas truce" of 1914
Source: Imperial War Museum
Alistair Carmichael has appeared to have ruled out a future bid for leadership of the Liberal Democrats.
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The British and German army football teams have played a match to commemorate 100 years since the World War One Christmas truce.