The Liberal Democrat leader also has claimed that the chances of Brexit falling through is now "maybe 20 per cent, possibly 25 per cent.”
He said: "The probabilities of having an exit from Brexit are rising because of the chronic weakness of the Government – the lack of ability to negotiate a satisfactory deal.
"We will almost certainly be faced with a poor deal, maybe no deal at all and I think under those circumstances, large numbers of, initially MPs, and then the public, wanting to revisit the basic question will rise.”
Speaking of the prospect of another referendum following last year’s historic vote to leave the Brussels bloc, Sir Vince said: "Hitherto I think most of them had said ‘forget it’. But they are beginning to realise that it is a very important potential mechanism.
"They were asking about the basic reasoning behind it, how it would work, what the question would be – it needs legal drafting, but the question would be do you … wish to accept Brexit as offered by the current Government, or do you wish an exit from Brexit and to remain a full member of the European Union?”
Sir Vince also revealed he is optimistic that peers across the House of Lords can join together to inflict a defeat on the Government over its EU Withdrawal Bill.
He explained: "Our people are fairly optimistic that on amendments of substance, particularly where this involves the rights of Parliament, the ‘Henry VIII powers’, they will be able to defeat the Government.”
Ministers are set to seek Parliament's backing to amend the EU Withdrawal Bill so that it explicitly states that the UK will leave the EU on March 29, 2019.
The idea was among those proposed by senior Labour MP Frank Field.
The Government has also said it is responding to MPs' concerns that the Bill's reference only to "exit day" meant the commitment would not be enshrined in law - which some fear would leave open the possibility of Britain lingering even longer in the EU.
It expects cross-party support for an amendment it has tabled to the Bill, which returns to the Commons for detailed line-by-line debate on Tuesday.
Brexit Secretary David Davis said: "Our amendment makes it crystal clear that the UK is leaving the EU at 11pm on 29th March 2019.
"We've listened to members of the public and Parliament and have made this change to remove any confusion or concern about what 'exit day' means.
"This important step demonstrates our pragmatic approach to this vital piece of legislation.
"Where MPs can improve the Bill, whatever their party, we will work with them."
The EU (Withdrawal) Bill will transplant thousands of EU laws into UK statute, to ensure businesses and people can operate as now from the day after Brexit while giving Parliament time to amend or repeal those it wants to change.