Speaking in Parliament on Tuesday, the Belgian MEP outlined a dramatic two-pronged plan designed to help relieve the suffering of up to two million mostly Syrian refugees.
This includes vastly increasing financial assistance to refugees trapped in camps in Turkey.
Under his plan, the monthly amount would increase from about €7 per refugee to €80.
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This would come from the €3bn pledged by the EU as part of its response to the crisis.
Another key plank of Verhofstadt's proposal is the creation of a rapid reaction force, comprising up to 2000 civil servants and agents, who would be despatched to refugee hotspots at short notice.
Speaking at a news conference in Strasbourg, the former Belgian Prime Minister said, "We need a new approach to tackling the crisis and this is our proposal."
EU interior ministers approved a European border and coast guard to stem migrant flows from North Africa and the Middle East.
The plan, put forward by the European Commission last December, must now be approved by the European Parliament, and then by the European Council at the end of June.
The EU coast guard will be built upon Frontex, the EU border agency that until now has had only coordinating powers, and it will be able to draw on at least 1500 experts that can be deployed in under three days.
But Verhofstadt believes this response is not fast enough to deal with the fast-moving refugee crisis.
He said, "It could be the end of the year before this fully comes into effect and that is simply too late. We need action now."
The reaction force would, he said, be tasked with managing the future influx of refugees and try to stem the flows heading to member states.
It would also have the job of distinguishing between economic migrants and asylum seekers.
At present, the UN oversees the distribution of financial aid to migrants and, under the ALDE plan, this would continue although the amount would be increased substantially.
This would take up €2bn of the €3bn pledged by the EU with the remaining €1bn going towards infrastructure projects, he said.
He added, "It is better to give the aid directly to refugees themselves rather than Erdogan (the Turkish president) and then not know what will happen to it."
The ALDE proposals were due to be discussed at a meeting between Verhofstadt, Commission First Vice President Frans Timmermans and the Dutch EU Council presidency.
Some 8000 people, many escaping the Syrian war, have arrived on boats from Turkey since March and are held under an EU deal with Ankara designed to seal off the main route into Europe for over a million people since 2015.
Under the deal, those who do not seek asylum in Greece - and those who are rejected - will be sent back to Turkey.
Between 1 January and 31 December 2015, an estimated 1,008,616 fled to Europe by sea. 84 per cent of them came from refugee-producing countries, with 49 per cent from Syria, 21 per cent from Afghanistan and nine per cent from Iraq.
Some 17 per cent were women and 25 per cent were children under the age of 18.
Aid teams provided more than 100,000 medical consultations to refugees and migrants on its search and rescue vessels in the Mediterranean Sea, in Italy, Greece, in the Balkans and in western Europe.
Despite winter conditions and attempts to close the sea route, people have not stopped fleeing and between January and April 2016, more than 180,000 people have arrived in Europe. More than 1200 people have died or gone missing in this same period.