CDU sources said Mrs Merkel has told her party she will not stand as a candidate for Chancellor or MP after 2021.
Mrs Merkel has been leader of the CDU since 2000, and Chancellor for 13 years, a period which has seen her dominate European Union and world politics.
After 13 years with Merkel at the helm, a lot of them in coalition with the SPD, many Germans are exhausted of government by carefully-crafted compromise, calling instead for clear direction on pressing policy issues like migration, security, reform of the European Union and climate change.
However she has come under mounting pressure in recent months, and her party suffered a disastrous result in state elections this weekend.
Just two weeks after Angela Merkel's Christian Social Union allies witnessed their worst election results in decades in Bavaria, her own Christian Democrats are experiencing déjà vu in Hesse's regional vote.
The CDU has governed Hesse for almost 20 years, and the party campaigned on an enviable record in the state of ultra-low unemployment, high wages and minimal crime.
Mrs Merkel has been CDU chairwoman since 2000 and giving up the role would start a race within the party to succeed her as chancellor. And the far-right Alternative for Germany was on course to enter the last of Germany's 16 state parliaments with more than 12%.
The nosedive in support for Merkel's party in Hesse, known as Hessen in Germany, was predicted by polls ahead of the crucial election.
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It is still unclear what this means for Merkel's leadership.
The German leader has also ruled out standing for a senior position within the European Union with speculation growing she wants to quit politics completely.
Such results would make various regional coalitions possible, with the Greens potentially joining parties to their right or left or even, if their results are exceptionally good, having a chance to make their local leader Tarek Al-Wazir - now Bouffier's deputy - the state governor. The party blamed its problems on federal-level politics, as SPD leader Andrea Nahles stated that the performance of the CDU/SPD grand coalition was one of the reasons for the crash and claimed that it was "clear that something has to change".
The CDU result marks a huge drop from the 38.3 percent won by the party during Hesse's last election in 2013.
CDU leaders will meet next Sunday to prepare for a summit in December where party members will vote for a new chairman.
With tensions high in the Berlin coalition, "no-one can say with 100 percent certainty how stable things will stay, what kind of dynamics will emerge in the individual parties" after the election, CDU general secretary Annegret Kramp-Karrenbauer said Thursday.
Merkel also reportedly said that she won't seek re-election to parliament after its current term ends, indicating that this will be her final term as chancellor - something that had been widely assumed but that Merkel has not until now confirmed.