An EU proposal would see Turkey offered financial aid and political concessions in return for taking back all migrants travelling to Greece.
EU leaders have watered down the incentives and correspondents say it is unclear if a deal can be done.
Nevertheless, Mr Davutoglu said he was hopeful of finding "common ground".
But he added that he wanted to keep a "humanitarian perspective" on the crisis.
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EU leaders agreed on a joint position to put to Turkey after late-night talks. The plan suggests that for every Syrian refugee sent back, another Syrian would be resettled in the EU directly from refugee camps in Turkey.
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Ahead of Friday's talks, German Chancellor Angela Merkel said that Turkey had to meet international standards of protection for all migrants.
She said that the legal resettlement of Syrian refugees could start a few days after the first returns from Greece.
However, she added that the EU needed to be ready to start returning migrants from Greece to Turkey rapidly to avoid a "pull factor" creating a surge of migrants before the new system takes effect.
Lithuanian President Dalia Grybauskaite warned on Thursday that the plan to return people to Turkey was "on the edge of international law" and difficult to implement.
But arriving at the summit on Friday she said an agreement was possible because "it is important and necessary for both sides".
Mr Davutoglu has said he will not accept Turkey becoming an "open prison" for migrants.
To meet concerns over the plan's legality, the leaders discussed providing assurances that each person claiming asylum will be given a full hearing in Greece, the BBC's Damian Grammaticas reports from Brussels.
Human rights group Amnesty International placed a large screen outside the Brussels summit that read: "Don't trade refugees. Stop the deal."
French President Francois Hollande warned that "I cannot guarantee that there will be a happy outcome" to the search for a solution.
Since January 2015, a million migrants and refugees have entered the EU by boat from Turkey to Greece. More than 132,000 have arrived this year alone.
Tens of thousands are now stuck in Greece as their route north has been blocked.
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