The former Deputy Prime Minister said Theresa May and Brexit Secretary David Davis could not achieve their goal of being a part of the trading bloc without conceding certain conditions.
Mr Clegg, MP for Sheffield Hallam, insisted there could be successful talks on immigration.
Speaking on Bloomberg, the former Lib Dem leader said freedom of movement was "eminently negotiable" but that the Government had put itself under pressure with unrealistic timeframes for the UK's future relationship with the EU.
Nick Clegg has said the Prime Minister and David Davis' demands were a "logical impossibility"
All politicians across Europe are dealing with electorates who are unsettled by immigration
He said: "I don’t think I’ve met a serious person who is involved with the negotiations who thinks you can do what the Government claims, which is settle the future arrangement between the United Kingdom and the EU in its entirety within a very short timescale.
"Expectations about the timetable have been set which won't be met. The fundamental problem is this, my own view has always been that the fraught issue of freedom of movement is eminently negotiable because it's actually a much more qualified freedom than many people say, it's much more elastic in the way in which governments can apply it.
"All politicians across Europe are dealing with electorates who are unsettled by immigration, so that is an entirely negotiable part of the picture.
"The bit that is non-negotiable is the assertion by Theresa May and David Davis that the United Kingdom will not under any circumstances respect the rulings of the European Union and the single market and yet it wants uninterrupted access to that single market. That is a logical impossibility."
EUROSCEPTICISM: These are the most eurosceptic countries Mon, January 16, 2017
EUROSCEPTICISM, meaning criticism of the European Union (EU). Rising disenchantment with the dealings of EU is not just confined to the UK.
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Meanwhile, a Lib Dem peer has told the Government to "bring it on" over a threat to abolish the House of Lords if it attempts to meddle with Brexit.
Lord Teverson welcomed the threat to scrap the upper chamber.
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He posted on Twitter: “So if the Lords messes with the Article 50 bill we'll be abolished, hmmm . . . bring it on #LibDems”
Theresa May is expected to start the formal process for Britain’s exit from the beleaguered EU by triggering Article 50 in one month.
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