Writing exclusively for The Independent, Mr Verhofstadt sends a clear and direct message to the Prime Minister that he wants the European Union to make a “generous” offer to people in the UK angry at losing EU privileges.
In response to his article a government spokesman has now said that Ms May and Brexit Secretary David Davis are actually ready to "discuss" any proposals that are put forward.
The European Parliament has already cemented into its formal negotiating guidelines its intention to explore what a potential offer to Brits might look like, with ideas including allowing them to opt in to a form of “associate EU citizenship”.
In his article, Mr Verhofstadt underlines the EU’s willingness to agree a quick reciprocal deal guaranteeing the rights of EU citizens in the UK and UK citizens in Europe, but he then moves on to the separate issue of offering rights to people in the UK who he calls “British Europeans”.
He cites the resolution passed by the European Parliament on Wednesday which notes that many UK citizens have “expressed strong opposition to losing the rights they currently enjoy” and commits the EU-27 to “examine how to mitigate this”.
The ex-Belgian prime minister writes in his piece: “I fought hard in the parliament for this provision to be maintained and hope in the coming months to continue to push for such an offer from the EU to British Europeans.
“The European Union will defend its interests in discussions with the British Government, but I also believe it is important the European Union is generous and open to British citizens.”
He adds: “I hope any such steps will be viewed openly by Theresa May.”
The Independent first reported European proposals last year to offer Brits “associate citizenship” of the EU, an idea which was then personally championed by Mr Verhofstadt.
The proposals began life as an amendment to a report by liberal Luxembourg MEP Charles Goerens, promising Brits who live and work across borders a way around the disruption caused by the Leave vote and young people looking to live in the EU more choice over where to move.
Despite some Brexiteers taking a dim view of the idea, seeing it as an attempt to undermine a clean break from the EU after Britain leaves, the government responded positively.
A spokesman told The Independent: "Securing the status of UK nationals in the EU and EU nationals in the UK, on a reciprocal basis, is a top priority for us as we enter into negotiations. We welcome the fact that our European partners are also prioritising this and will be seeking the earliest possible agreement on this issue.
"As for future arrangements, these will be subject to discussion. Naturally we will discuss any ideas that are put forward."
The Tory grandee reacted after European Council President Donald Tusk placed a note in the EU’s draft negotiating statement that suggested Spain could veto any Brexit deal affecting the status of the British territory.
Mr Verhofstadt writes in his piece: “Within days of Article 50 being tabled we were reminded of the important role the EU has played in unifying European nations, when some who should know better compared Gibraltar to the Falkland islands and suggested the British Prime Minister would be justified in taking military action against Spain, despite the fact that no one threatened the sovereignty of Gibraltar.
“Yes, it is inevitable that the EU will now support the economic interests of Spain and the Republic of Ireland in any forthcoming discussions about the EU’s external borders, but in the coming years the EU’s interest will be to secure peace on our continent, not stoke division.”
Mr Verhofstadt went on to pour cold water on Ms May’s plans to secure access to the single access to specific sectors, like finance firms in the City of London or the automotive industry.
He added: “As the Parliament’s Brexit text also makes clear, any future economic agreement between the European Union and the United Kingdom must not contain piecemeal or sectorial provisions regarding preferential access to the single market.
“This is not punishment, it is an inevitable consequence of the UK Government’s decision to leave it.”
Instead Mr Verhofstadt suggest the deal brokered between the EU and Ukraine could provide an “appropriate framework for a special future relationship” with Britain.
The Strasbourg parliament’s formal negotiating guidelines will now feed into the overall mandate handed to chief EU negotiator Michel Barnier after a meeting of the European Council on April 29.