The SPD would have 16 percent of the voters backing them, while their partners in the ruling coalition, the union of the CDU and the CSU, could jointly gather 28.5 percent of the vote, a poll by INSA for Bild showed Monday.
The Greens might hope for 13.5 percent of the vote.
On August 28, an INSA poll had the SPD and the AfD tied for the second place with 16 percent of the vote each, potentially.
Germany has been facing a number of migration-related issues this year, starting from the disagreements between the CDU and the CSU, which almost led to the resignation of Interior Minister Horst Seehofer, the leader of CSU, urging for a tougher immigration policy.
More recently, the city of Chemnitz in East Germany has seen several right-wing rallies and counterprotests, following the killing of a German citizen. The police have detained two suspects of Iraqi and Syrian origin.