Ms Le Pen and her Front National have made clear their desire to hold a referendum on France's EU membership – a move which could trigger an existential crisis for Brussels.
A poll released on Monday gave Ms Le Pen the lead as France prepares for elections in the spring.
Interviewed on LBC, Mr Verhofstadt, who is the European Parliament's chief Brexit negotiator, refused to consider the idea of Ms Le Pen coming to power.
Speaking to Matt Frei, the former Prime Minister of Belgium scoffed at the idea of the Front National winning this year's elections.
"If Marine Le Pen becomes the president of France, you can kiss the European Union goodbye," Frei told the MEP.
The former Belgian Prime Minister replied: “Will not happen, will not happen.”
Marine Le Pen's election could trigger a collapse of the EU
Frei then reminded his guest how he had previously ruled out Brexit and Donald Trump winning the US election.
“I do not believe that Le Pen win in France,” Mr Verhofstadt insisted.
“I am very confident of the fact that especially in Europe we are going to see a rebirth and a re-foundation of the European Union.
Marine Le Pen will run in the French Presidency in the election which takes place in April
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I do not believe that Le Pen win in France
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“Nationalism and populism is already an old movement in Europe.”
The 48-year-old, the daughter of former Front National leader Jean-Marie Le Pen, is hoping to harness the anti-establishment and populist mood which aided the Brexit vote and Mr Trump's election.
Speaking at a gathering of right-wing leaders in Germany last week, Ms Le Pen said Britain’s decision to leave the EU would have a domino effect across the Continent.
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She said: "2016 was the year the Anglo-Saxon world woke up. I am sure 2017 will be the year the people of continental Europe wake up.”
"We are experiencing the end of one world and the birth of another.
"I don't say every country has to leave the euro… But we have to leave the possibility if a country wants to leave.
“The key factor that is going to set in course all the dominos of Europe is Brexit. A sovereign people chose … to decide its destiny itself.”
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