The former Belgian prime minister is one of three so called MEP "Sherpas" tasked with negotiating David Cameron's proposed EU settlement on behalf of the European parliament's main political groups.
Verhofstadt wants EU leaders to agree to change the bloc's treaties to allow the UK to benefit from an arrangement that would acknowledge and guarantee "the special status of Great Britain" as an EU member state that doesn’t want to deepen integration.
The Belgian Liberal group deputy told reporters following his meeting with the British prime minister on Tuesday that it was important both economically and geopolitically for the UK to stay in the EU.
"I think that the only two people that would gain from a Brexit are Nigel Farage and Vladimir Putin because the aim of both of them is to divide Europe."
"If Britain doesn’t want to be associated with further political integration then so be it. That's the choice of the British government and of the British people. But let's then recognise that and put it in the treaties."
"Let's recognise that this is already the case today, that the UK is not part of the euro, that it is not part of Schengen, that the UK is not part of a number of policies in the union."
The contentious preamble on "creating an ever closer Union" in the EU treaty has been a flashpoint of the UK's renegotiations. Verhofstadt believes that granting the UK special status to opt out of further political integration, would satisfy British concerns while allowing the remaining EU member states to deepen "the integration that is desperately needed by the bodies of the EU".
"David Cameron is asking for reforms in the EU. We are in favour of reforms in the EU. So we are very much in favour of a deal, of an agreement where Europe's leaders recognise the special status of Great Britain in the European Union."
"This is the way to solve this (problem) because at the same time we need ourselves changes in the treaties. It's a win-win situation."
He also offered up words of encouragement to David Cameron as the British prime minister sought to obtain guarantees from the European Parliament's leading policymakers that any settlement would not be overturned by MEPs.
Verhofstadt said the parliament would be "open and constructive" on delivering the secondary legislation that would be needed following any deal on introducing an so-called 'emergency brake' on in work benefits for EU migrants, but that neither he nor anyone else in the parliament could guarantee that the assembly would not seek to alter any deal agreed by EU leaders
"We have given the assurance that the European parliament will be open and very constructive. We have even said to him, we are ready to strengthen the agreement in the sense that we recognise that there should be for Britain special treatment in the treaty recognising that they don’t want to go further in deepening political integration. To put that in the treaties is a major achievement for Britain."
"I think David Cameron came out of the meeting with more confidence than before. I think there will be an agreement. It's now up to Europe's leaders on Thursday to find the final agreement around these lines."