0530 GMT January 28, 2020
The proposals came after a sharp rise in new arrivals from the two countries and public outrage over a rash of attacks on women on New Year's Eve in the western city of Cologne blamed on North African and Arab migrants, Yahoo reported.
Welt am Sonntag newspaper reported that Chancellor Angela Merkel and Bavarian state leader Horst Seehofer had agreed that Algerian and Moroccan asylum seekers should no longer be put in shelters throughout the country.
Instead, they would be housed in existing expulsion facilities in Bavaria until their claims have been heard, similar to the practice currently used for applicants from Balkan countries who are unlikely to be granted asylum.
Vice Chancellor Sigmar Gabriel noted Sunday that this option could be applied more widely.
Germany has said it wants free up resources to help people fleeing war-ravaged countries such as Syria.
Albania, Bosnia, Kosovo, Macedonia, Montenegro and Serbia have all been declared safe countries of origin by Germany, meaning their citizens have very little chance of gaining refugee status.
Berlin plans to add Algeria and Morocco to the list.
The numbers of Algerian asylum seekers arriving in Germany rose to 2,296 in December from 847 in June, while those from Morocco jumped to 2,896 from 368, the Interior Ministry said.
"A good case can be made for placing migrants from the North African region without a chance of staying (in Germany) in repatriation centers," an official from Seehofer's Christian Social Union, Thomas Kreuzer, told Welt am Sonntag.
Seehofer is the most vocal critic of Merkel's liberal refugee policy within her conservative bloc and has pressed for her to set an upper limit on the number of asylum seekers entering Germany.
Merkel has rebuffed these calls, dismissing them as impractical and unconstitutional.
But pressure on Merkel has grown since the Cologne melee, which gave rise to more than 670 criminal complaints including over 330 relating to sexual violence.
About 50 kilometers (30 miles) from Cologne in Duesseldorf, police said they had detained 40 men from North Africa, nearly all on suspicion of being in Germany illegally, following raids Saturday in the so-called Maghreb Quarter notorious for pickpocket and drug gangs.
The head of the Duesseldorf operation, Frank Kubicki, said it had been planned before the events in Cologne.
"At the same time, we expect findings that could aid the (Cologne) investigation," he said.