European Council President Donald Tusk is due to hold talks with Turkish President Recep Tayyip Erdogan to try to strengthen their joint approach to Europe’s migration crisis.
Mr Tusk has raised the idea of “shipping back” migrants who arrive in the Greek islands from Turkey.
He said on Thursday that it could break the business model of people smugglers.
Mr Tusk has been engaged in intense diplomatic activity ahead of an EU-Turkey summit to be held on Monday.
French President Francois Hollande is also hosting the German Chancellor Angela Merkel in Paris on Friday to discuss the migration crisis.
Thousands of refugees and migrants are continuing to arrive on the Greek islands every day after setting off from the Turkish coast.
They aim to reach Germany and other countries in northern Europe but are finding their way blocked by increasing border controls.
More than 25,000 are now stranded in northern Greece on the border with Macedonia, raising fears of a humanitarian crisis.
BBC Europe Correspondent Chris Morris says Mr Tusk’s talks with President Erdogan on Friday are crucial if the flow of migrants to Europe is to be stemmed.
On Thursday, Mr Tusk warned illegal economic migrants against coming to Europe.
“I want to appeal to all potential illegal economic migrants wherever you are from: Do not come to Europe,” he said after talks in Athens with Greek Prime Minister Alexis Tsipras. “Do not believe the smugglers. Do not risk your lives and your money. It is all for nothing.”
Later, after meeting Turkish Prime Minister Ahmet Davutoglu in Ankara, Mr Tusk said the number of migrants crossing the Aegean Sea from Turkey to EU states remained “far too high”.
He said it was for Turkey to decide how best to achieve such a reduction but added: “To many in Europe, the most promising method seems to be a fast and large-scale mechanism to ship back irregular migrants arriving in Greece.
“It would effectively break the business model of smugglers.”
Mr Davutoglu said the flow of Syrian refugees would lessen if the cessation of hostilities in the conflict held.
The crisis has threatened the future of Europe’s passport-free Schengen zone as countries reinstate border controls to stem the flow of people.
Sources in Brussels say the EU will unveil a “roadmap” on Friday outlining a plan to restore the zone to full force by November.
A draft seen by AFP news agency includes strengthening Greece’s external borders and quickly creating an EU coastguard system.
The International Organization for Migration says 120,369 migrants have arrived in Greece from Turkey so far this year and at least 321 have died en route.
On Thursday, a group of migrants blocked a railway line on the Greek side of the border with Macedonia in protest at restrictions stopping them moving north.
The restrictions were imposed after several Balkan countries decided only to allow Syrian and Iraqi migrants across their frontiers. Austria also decided to limit numbers.
The move effectively barred passage to thousands of people seeking to reach western Europe, including Afghans as well as some more likely to be regarded as economic migrants.
“I know the border is closed but I want to go to Germany,” said Mohamed, an Egyptian.
“I will try, try, try. Egypt is bad, there is no work.”
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.