Turkish President Recep Tayyip Erdogan was to meet Monday with the EU's top officials for urgent talks on the migration crisis and the Syrian war that is producing so many of the refugees.
Erdogan's visit comes as it emerged that 630,000 people have entered the European Union illegally this year, many coming via Turkey, and that Germany could receive up to 1.5 million asylum-seekers in 2015.
Facing the worst refugee crisis since World War II, Brussels and Ankara are reportedly set to discuss a plan that would see Turkey join Greek coastguard patrols in the eastern Aegean, coordinated by EU border agency Frontex.
Any migrants picked up would be taken back to Turkey, where six new camps for up to two million people would be built, co-financed by the EU, to relieve the huge pressure on Greece in particular.
European officials are also set to push Turkey to tackle people smugglers, a scourge that was once again in the spotlight on Sunday when the badly decomposed bodies of two children were found washed up on the Greek island of Kos.
But officials played down the chances of a final deal on the plan during the visit by Erdogan, saying the talks were likely to be "difficult" and that they would probably only mark the formal start of the process.
The Turkish leader was due to meet later Monday with European Council President Donald Tusk, European Commission President Jean-Claude Juncker and European Parliament chief Martin Schulz.
- Turkey to press EU on Syria -
The migrant crisis has further taxed relations between Erdogan and Brussels, long strained by EU criticisms of Ankara over human rights and by tortuous negotiations on Turkey's application for membership of the bloc.
Erdogan -- whose country hosts around two million refugees from the conflict over the border in Syria -- is expected to press the EU for more help in ending the war and for his fight against Kurdish rebels.
The Turkish leader, a strong opponent of Syrian President Bashar al-Assad, is likely to push his plans for a no-fly "safe zone" over northern Syria where refugees could be housed.
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But Western officials have cast doubt on the plan, and those doubts will be reinforced after Turkey said on Monday that its jets had intercepted a Russian fighter plane that violated Turkish airspace just days after Moscow launched air strikes in Syria.
Syrians make up the largest group of people seeking asylum in Europe, followed by Afghans.
The migration crisis has reached such a scale that Germany could receive up to 1.5 million asylum-seekers this year, according to newspaper Bild, quoting a confidential document with estimates far higher than official figures.
Frontex chief Fabrice Leggeri said 630,000 people have entered the bloc illegally this year.
He called for 775 extra border guards to be deployed at the EU's external borders -- the largest request in Frontex's history -- to beef up defences in Italy and Greece.
- Children's bodies washed up -
On Greece's Kos, the body of a dead baby boy, thought to be less than a year old, was discovered on a hotel beach early Sunday, dressed in green trousers and a white T-shirt.
The decomposed body of another child, wearing blue trousers and a pink T-shirt and believed to be three to five years old, was found hours later at the same spot.
The case revived memories of Aylan Kurdi, the three-year-old Syrian refugee whose body was washed up on a Turkish beach while his family tried to get to Greece, producing pictures that shocked the world.
Greece's coastguard fears the problem will worsen as winter approaches.
The flow of migrants also continued through the Balkans -- with many initially landing in Greece and then moving on towards Germany, despite EU rules stipulating that asylum-seekers should be dealt with by the first country in which they arrive.
A total of 5,800 crossed into Austria from Hungary on Sunday, plus another 2,500 between midnight and Monday morning, official figures showed. A further 5,925 crossed into Hungary illegally on Sunday, almost all via Croatia.
The huge influx of people has exposed deep rifts among the EU's 28 member states.
EU leaders agreed at an emergency summit last month to share 160,000 migrants throughout the bloc, but several member states opposed the plans, while mooted "hotspots" on Europe's borders have proved controversial.