The former Cabinet minister, who is the only candidate to replace Tim Farron as Lib Dem leader, said he believed Mr Corbyn’s popularity would dwindle as the young voters he had inspired realised the Labour leader backed a “hard” Brexit.
Sir Vince also said he backed “moderate” tax increases, arguing that measures to balance the books needed to shift away from swingeing cuts.
The former business secretary, who returned to the Commons at the general election after regaining his Twickenham seat, highlighted divisions within the two largest parties.
Asked if critics of Labour leader Mr Corbyn at risk of being ousted by left-wingers would be welcomed to the Lib Dems, Sir Vince said: “We have a generous policy to refugees and if they come they will get food and accommodation.
“I don’t know what will happen, it’s a symptom of very, very deep division.”
Mr Corbyn had a good election but “there is an element of a bubble about it” because “actually he is very pro-Brexit, and a hard Brexit, and when that becomes apparent the divisions in the Labour Party will become more real and the opportunity for us to move into that space will be substantial”.
Sir Vince told BBC’s Andrew Marr Show: “There is an imminent issue, which is whether the Government continues to pursue the so-called hard Brexit - leaving the customs union and single market.
“We have got to work with other people, we did last week, there was a motion in Parliament led by some Labour MPs we supported, to try to head of that disastrous outcome.”
If the economy suffers, people will reconsider Brexit and “the whole question of continued membership will once again arise”.
He said: “I’m beginning to think that Brexit may never happen. The problems are so enormous, the divisions within the two main parties are so enormous I can see a scenario in which this doesn’t happen.”
Even though he is not expected to face a challenger in his bid for the leadership, Sir Vince said he would still produce a manifesto - and suggested he would support tax rises beyond the 1p income tax hike which the party proposed at the election to pay for health and social care.
He said: “I certainly want to shift the balance away from extreme cuts on public services, which are particularly harsh in local government, and have a bit more tax to balance it.
“I would also have more financing of public capital investment for housing.”
Sir Vince has come under fire for claiming Theresa May’s rhetoric on “citizens of nowhere” was like something from Hitler’s Mein Kampf.
He admitted he had compared her to the wrong murderous dictator: “I got my literary reference wrong - I think it was Stalin who talked about ‘rootless cosmopolitans’.”