“That is being looked at closely in our ministry,” Interior Minister Horst Seehofer told newspaper group RedaktionsNetzwerk Deutschland (RND) on Friday.
Tens of thousands of Syrians have sought asylum in Germany, with the biggest influx taking place in 2015.
A ban on expulsions to Syria has been in place as war rages there, but the restriction runs out at the end of the year.
Germany would then need to consider whether to extend the ban, and the foreign ministry's assessment of the situation in Syria would be crucial in the decision.
But several high-profile crimes involving migrants have soured the public mood in Germany, prompting interior ministers of several states to push for the expulsion of asylum seekers who have been convicted.
“Once the security situation allows, dangerous individuals and criminals can be sent back to Syria,” Saxony state's interior minister Roland Wöller told RND.
Idlib and some surrounding areas are the last major rebel bastions in Syria, where the Russian-backed government has in recent months retaken much of the territory it had lost since the civil war erupted in 2011.
Berlin in 2016 signed a controversial deal with Kabul to repatriate Afghans who had failed to obtain asylum, even though Afghanistan remains strangled by violence.
The news has come after high profile crimes involving asylum seekers and refugees in Germany have sparked protest.
In Freiburg recently, the alleged gang rape of an 18-year-old woman by a group of men that included Syrians resulted in an Alternative for German (AfD) group organizing calling for better security in the country.
However, they were met by a far bigger counter-protest which accused the AfD of using the crime for its gain.