The latest figures reveal that more than 125,000 migrants and refugees have arrived in Europe so far this year
EU leaders say they have been unable to agree a deal on a Turkish plan for resolving the migration crisis.
They had been discussing an idea that all migrants arriving in Greece would be sent back to Turkey.
In return the country would get more than €6bn in aid - and a deal over visas for its citizens.
Turkey is currently in talks about joining the EU.
But it has come in for criticism over the government's takeover of a leading opposition newspaper.
The latest draft proposal says that Turkey will take back all irregular migrants who arrive in Greece from a certain yet-to-be-determined date, Sky News reports.
The second part of the deal would see the EU admitting genuine refugees on a one-for-one basis: every irregular migrant Turkey takes back will mean that the EU will accept a refugee.
Turkish Prime Minister Ahmet Davutoglu earlier told the talks in Brussels: "With these new proposals we aim to rescue refugees, discourage those who misuse and exploit their situation and find a new era in Turkey-EU relations."
In exchange, Turkey would get €6bn to help Syrian refugees stay in Turkey, faster visa-free travel for its citizens and renewed talks aimed at granting its membership of the 28-country bloc.
Sky News Europe Correspondent Mark Stone said: "It appears that the Turkish prime minister, on behalf of his president, has come to Brussels today to drive a particularly hard bargain.
"In practise, it's hardly very achievable with the current number of arrivals. But it's a neat way of sending a message to migrants and refugees not to come."
Stone said Turkey wants to use the money to improve conditions for refugees remaining in the country.
"If it can get that money from the EU then the result of that will be to stem the flow, because these people will be happy to remain in Turkey, instead of coming to Europe."
The latest figures reveal that more than 125,000 migrants and refugees have arrived in Europe so far this year. It is estimated around 2,000 are crossing into Greece each day.