BERLIN—Germany is considering a push for European sanctions against Russia in response to its actions in the Syria conflict, a person familiar with the German deliberations said Wednesday, signaling that Europe is seeking new ways to pressure Moscow to quell the violence there.

Chancellor Angela Merkel’s government, the person said, is examining ways to push Moscow to change course in Syria, where Russian warplanes have supported Syrian government forces in a siege of rebel-held areas in the city of Aleppo.

Western leaders are calling the situation an increasingly grave humanitarian crisis. German and U.S. officials have said Russia is behind some of the bombardment of hospitals and other civilian installations in Aleppo.

One action Germany is considering, the person said, is implementing new European Union economic sanctions against Russia. Two years ago, Ms. Merkel, the EU’s most influential leader, corralled the bloc’s 28 countries to impose joint sanctions against Russia over its military intervention in Ukraine.

The deliberations among German officials on possible sanctions are in their early stages, and it’s not clear how broadly Ms. Merkel’s junior coalition partners, the center-left Social Democrats, would support them. But they are among the first signs that Europe, frustrated by Russia and fearful of a worsening of the refugee crisis, could swing to a tougher line.