According to a person at the meeting, chancellor-in-waiting Social Democrat Olaf Scholz presented the EU's longest-serving leader with a tree to plant in her garden.
As finance minister and vice chancellor in the outgoing "grand coalition" of the SPD and conservatives, Scholz, 63, was seen as a competent rather than a charismatic politician who, like Merkel, has moderate views and is adept at dialogue.
The main obstacle in talks were divisions on how to finance the transition towards a green economy and how quickly to move, according to party sources.
Such frictions could persist as it is widely expected that FDP leader Christian Linder, 42, will take over at the finance ministry and Greens co-leader Robert Habeck, 52, will take on a newly expanded economy and climate change ministry.
The FDP is also expected to put the brakes on any formal move towards fiscal union in Europe favoured by the SPD and the Greens.