The European Parliament's chief negotiator revealed he wants rival party leaders to sign up to the PM's top team in Brussels.
And in an apparent push for a role for Mr Corbyn, he described last month's election result as an "own goal" for Mrs May.
He said British voters had "rejected" her Brexit plans and more "diverse" voices should be listened to.Related articles
Brexit is about the whole of the UK, it's about people's lives
Mr Verhofstadt said: "Brexit is about the whole of the UK. It will affect all UK citizens, and EU citizens in the UK.
"This is much bigger than one political party’s internal divisions or short term electoral positioning.
"It's about people's lives."
GETTY•REUTERSGuy Verhofstadt wants rival party leaders to join May's Brexit negotiating team
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France has the highest score in the index at 32.5