Etihad, which owns a 29 percent stake in Air Berlin, is under investigation by German and European authorities over its partnership with Germany's second largest airline after Lufthansa.
For Air Berlin to maintain its European operating license, it must be majority controlled by European investors.
Without citing its sources, Focus said Merkel told Transport Minister Alexander Dobrindt at a cabinet meeting that she did not want to "dig the grave" of Air Berlin and that Germany needed competition between two strong national carriers.
The German government declined to comment on the report.
Dobrindt will only make a decision on Etihad's involvement in Air Berlin early next year, the Wirtschaftswoche weekly reported on Saturday, citing sources at the transport ministry.
The Wirtschaftswoche cited an unnamed source at Lufthansa as criticizing the delay in reaching a decision.
Last month, the German federal aviation authority (LBA) suspended a decision to block Etihad from selling tickets for some flights operated by Air Berlin.
The LBA checks codeshare deals every time airlines submit winter and summer schedules for flights to and from Germany.
Deutsche Lufthansa has said it would not fly between Abu Dhabi and Frankfurt in the summer of 2015 because it had become uneconomical due to overcapacity it blamed on Etihad and Air Berlin, calling their code shares "unjustified."