The Frankfurter Allgemeine Sonntagszeitung said the European Commission and Turkish government representatives struck the accord last week and that it would be approved during talks Monday in Brussels between Turkish President Recep Tayyip Erdogan and EU leaders.
Under the plan, Turkey would agree to stepped-up efforts to secure its frontier with the EU by taking part in joint patrols with the Greek coastguard in the eastern Aegean coordinated by EU border protection agency Frontex, the report said.
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.
EU states meanwhile would agree to take in up to 500,000 people to ensure their safe passage across the sea without the involvement of people smugglers.
The report, citing Commission and German sources, said the plan fleshed out a preliminary 2013 agreement between Brussels and Ankara.
Assuming there is an accord Monday, the plan would go before EU leaders at the next summit in mid-October.
The EU has long called on Turkey to do more to stem the tide of migrants making the dangerous crossing to Greece, with more than 500,000 having made it to Europe's shores this year.
EU leaders agreed at an emergency migrant summit last week to offer more aid to Ankara as well as other countries in the region.
But the EU believes Ankara could do more to tackle what it says are some 30,000 people smugglers in Turkey.
It also wants to set up "hotspots" for registering asylum seekers on Turkish soil -- a measure recently ruled out by Prime Minister Ahmet Davutoglu.
Turkey is currently hosting almost two million Syrian refugees.