News agency DPA cited unnamed sources within Germany's ruling party on Monday morning that Dr Merkel, who has led the CDU since 2000 and has been Chancellor since 2005, would be stepping down in December in time for party conference. "We haven't heard about serious contenders to replace her".
Merkel standing down from the party chair would allow a new CDU chairman or chairwoman to build a profile before the next national election.
However, the SPD's historic losses could mean yet more pain for the chancellor's already troubled government coalition in Berlin.
The CDU won about 28% of the vote there on Sunday, down from 38% five years ago.
Ms Nahles is also feeling the heat from party members still disgruntled with her decision to join Ms Merkel instead of fulfilling an election promise to sit in opposition if they fail to win the federal vote.
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Following the close election results, the SPD's leader, Andrea Nahles, has announced a mid-term review of the current coalition government next year, taking the declining voting numbers as a sign that the German electorate is growing exhausted of the coalition's constant in-fighting and lack of progress on bringing legislative change to Germany.
In Hesse, where Merkel's CDU rule with the ecologist Greens, the two biggest winners were the Greens and the far-right Alternative for Germany. The result, the SPD's worst since 1946, will pile pressure on the party leader, Andrea Nahles.
The CDU's general secretary, Annegret Kramp-Karrenbauer, said the coalition needs to identify "three concrete projects for the coming months that we implement". On October 14, the Christian Social Union, or CSU - the Bavarian sister party to the CDU - lost its majority in the Bavarian state parliament.
Voters have appeared generally satisfied with Bouffier's outgoing state government.
She is understood to have said she intends to continue as Chancellor until 2021 when her current term finished.
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Chancellor Angela Merkel's Christian Democrats have suffered huge losses on Sunday in regional elections in the central German state of Hesse.
A senior CDU member told Reuters that party leaders wanted to discuss the possibility of Merkel reversing her decision to seek re-election as party chairwoman in December.
"Secondly, this fourth term is my last as German chancellor".
The unexpected reversal by Merkel, 64, signals the beginning of the end of an era during which her command of Germany put its stamp on Europe and beyond for more than a decade. According to Deutsche Welle, as news of Merkel's move spread, Christian Lindner, who leads the center-right Free Democrats (FDP), said, "She's quitting the wrong office".
For a start, Mrs Merkel's coalition...
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