Turkey last month stopped German MPs from visiting their troops stationed at the Incirlik base in southern Turkey, which is used to launch coalition raids against Islamic State (IS) jihadists in Syria.
After meeting Turkish President Recep Tayyip Erdogan at the G20 summit in China, Merkel said she was hopeful of progress on the issue.
"I think it is possible that in the coming days we will have good news about this completely justified request," Merkel said.
The airbase ban came with tensions running high between Berlin and Ankara over a resolution by the lower house of the German parliament calling the mass killing of Armenians by Ottoman forces during World War I a genocide.
Turkey vehemently rejects the genocide claim, arguing it was a collective tragedy in which both Turks and Armenians died.
The German government has stressed the Bundestag vote was non-binding, a move widely interpreted as a step to soothe Ankara, a key player in both the fight against IS and the European migrant crisis.