Merkel, who faces a national election in September, has called repeatedly for a "national effort" to make sure that people without the right to stay leave the country.
Deportations currently are handled by state governments, but top officials have recently made clear the federal government wants more influence.
After the meeting yesterday, Merkel and the governors told reporters in Berlin that they would work closely to devise new deportation regulations, German news agency dpa reported.
The officials also want to establish a national center to coordinate returns.
According to the developing plans, people with few prospects of getting asylum would be processed and deported only weeks after their arrivals in Germany.
Immigrants who agree to return to their home countries voluntarily without waiting for their applications to be reviewed would receive financial incentives.
In 2016, some 55,000 asylum-seekers left Germany voluntarily and about 25,000 were deported. Also last year, 280,000 people requested asylum, compared to 890,000 in 2015.
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