"We'll manage to do it a few days earlier," in a good signal to those concerned about migration, Peter Altmaier, head of the Chancellery, told public broadcaster ARD.
The law had originally been slated to come into force on November 1st.
But the sped-up timetable could see the first deportations of people whose asylum applications were rejected take place early next week.
"We want to get better, get better quickly, within this year, at deporting those whose applications have been refused and who have no right to stay here," Altmaier said.
Tough new rules
MPs from Merkel's governing coalition voted through the hard-fought law last week.
Among other measures, it defines western Balkan countries Albania, Kosovo and Montenegro as 'safe countries' whose citizens won't be able to apply for asylum.
The new rules also reduce the amount of cash benefits given to asylum seekers while their applications are being considered, replacing them with 'in-kind' support.
The tightening of rules in Germany comes as Sweden, the EU country that takes in the most refugees as a proportion of its population, also announced it was toughening asylum laws on Friday.
Both Germany and Sweden have been fighting for a fairer distribution of asylum seekers across the 28-member union in recent weeks.