Immigration is expected to be another key point of contention.
The SPD opposes a conservative plan to extend beyond March a temporary halt on the right of some accepted asylum seekers to bring in family members.
It says the measure hampers efforts to integrate the 1.6 million people who entered Germany seeking asylum in 2015 and 2016. "Integration works only with families," Klingbeil said.
Merkel's CDU hold a meeting on Monday to discuss the looming coalition talks, which also face a threat from strains within Merkel's conservative bloc.
The CSU, which fears losses to the far-right Alternative for Germany (AfD) in an election in Bavaria next year, is likely to put up more resistance to SPD policy demands than the CDU, notably on immigration.
"After a result of 20.5 percent, you simply cannot continue on the same path, and many issues have to be solved," SPD deputy leader Ralf Stegner told Bayern 2 radio. "It is not certain this will work with the Union, where the CDU and CSU are quarrelling."
