"There is a major engagement on the part of Greece and Turkey towards sending 500 people back on April 4, barring a last-minute problem," the source told AFP on Thursday, though Athens and Brussels later declined to confirm how many would be sent back.
Those returning will be "Syrians who have not requested asylum, Afghans and Pakistanis", the official added, confirming that this is the first return set to take place under the EU-Turkey deal.
In Brussels, EU spokeswoman Natasha Bertaud confirmed that Monday was the "target day" of the new EU-Turkey scheme for "the return of asylum claims that have been declared unadmissible because they can get protection in Turkey and the start of the resettlement of Syrians from Turkey in the EU."
A Greek government source said the returns would "most probably" occur from Chios or Lesbos -- the islands that have handled the bulk of arrivals from Turkey, and where thousands of migrants are being held in overcrowded registration centres.
More From This Section
"We do not exclude that certain people will be returned Monday but we cannot confirm that it will be this kind of number," the official said.
Greece's deputy defence minister Dimitris Vitsas earlier this week said the returns to Turkey would take place "on six ships chartered by EU border agency Frontex."
However, a Frontex spokeswoman told AFP on Thursday that the agency was "not active" in the process for the time being.
"The procedures between Greece, Turkey and the European Commission are still being finalised, we are not active in the returns process yet," Frontex representative Paulina Bakula said in an emailed statement.
This includes over 11,000 people at Idomeni on the Greek border with Macedonia and some 5,700 at the port of Piraeus near Athens, waiting in vain and increasing desperation for Balkan states to open their borders and permit them passage to affluent northern Europe.