Merkel's spokesman Steffen Seibert said the talks would "likely take place tomorrow", a day before Group of 20 leaders meet in the northern port city of Hamburg.
Bilateral relations have been fraught, deteriorating sharply over Turkey's mass crackdown after a failed coup last year and a host of other civil rights controversies.
Ankara last week reacted angrily after Berlin refused to allow Erdogan to address members of the large ethnic Turkish community in a rally in Germany ahead of the G20 summit.
The installation was set up outside Merkel's offices in Berlin on Monday, comprising a Mercedes C-class car and banners with pictures of Erdogan, Russian President Vladimir Putin and Saudi King Salman.
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