Speaking in Brussels, Clegg said this was the "most likely" outcome, adding "it's the one I would put my money on."
His comments came on the day the Supreme Court in the UK ruled that the Westminster Parliament must give its approval before article 50 is triggered.
The judgement means UK Prime Minister Theresa May cannot begin talks with the EU until MPs and peers give their backing - although this is expected to happen in time for the government's 31 March deadline.
Clegg believed there are three possible outcomes to Brexit, one being that British withdrawal does not actually happen.
"This is only possible in the unlikely event of the British public having a change of heart and realising that the promises by the Leave camp, such as on the NHS, that were made will not be fulfilled."
The second possible result, he said, was an "orderly and structured" exit. For this to happen, a "new relationship", possibly an association agreement, between the EU and UK would be necessary.
However, Clegg, who spent five years as an MEP, predicted a "chaotic" withdrawal because, he said, the Brexit plan proposed last week by May was "implausible" and "unenforceable."
There was a direct contradiction, he said, between May's desire for free trade deals and her "determination" to "turn her back on the single market, the world's most successful free trade zone."
"She will not be able to have her cake and eat it," he forecast.
In order to avoid a "disorderly" exit, he said May must do one of two things: either "compromise her hard line" approach or continue to advocate a so called 'hard Brexit' under which the UK would also leave the single market.
"I hope she goes for compromise, but only time will tell," Clegg told a conference on Europe's future, organised by Forum Europe.
Clegg, a Liberal MP, also warned of "massive disruption" to the UK in the coming years.
With May due to meet US President Donald Trump in Washington on Friday, the first foreign leader to meet him since his swearing in last Friday, Clegg also said he hopes the Prime Minister will avoid the "cringe-worthy sycophancy" previous British premiers had shown American presidents.
"It would also be a fundamental mistake for the UK to become involved in a wider ideological conflict," he told an audience that included several MEPs.