Chancellor Angela Merkel is under growing pressure over her handling of the crisis, with her popular support waning and some in her conservative party wanting upper limits on migrants, the report says.
Her government has long said it wants to speed up the processing of asylum applications and that anyone who is rejected must leave, but there is a big backlog in deportations.
"If (economic grounds) is the only reason for being here, then we will have to say more strongly to these people: you must go home," Merkel said at IG Metall union event in Frankfurt.
The government has discussed a range of options, including using army transporters to help deport people, not telling individuals in advance that they would be sent home and tightening up rules that let some failed asylum seekers stay.
"Sending people back on commercial airlines takes priority but if there is insufficient capacity then... we will consider making use of military aircraft," government spokesman Steffen Seibert told a government news conference.
Germany is struggling to cope with an influx of about 10,000 migrants a day and expects at least a total of 800,000 this year.
