German Chancellor Angela Merkel attends a news conference following the Hesse state election in Berlin, Germany, October 29, 2018.
German Health Minister Jens Spahn is reportedly throwing his name into the hat as a candidate to succeed Merkel as leader of the party.
Ms. Merkel, 64, who is in her fourth term as chancellor, gave no indication that she would also step down as head of government.
While the CDU remained the largest party in the election, which was held in the central state of Hesse, its vote was down 10% from the previous election.
The ARD exit poll showed only 13 percent of CDU voters believed Merkel had helped the party in Hesse, down from 70 percent at the last state election, reflecting voter anger at her decision in 2015 to welcome nearly one million, mainly Muslim asylum seekers.
Merkel standing down from the party chair would allow a new CDU chairman or chairwoman to build a profile before the next national election.
"The naked numbers of the results in Hesse are very disappointing and bitter and it doesn't help that this state election was just a state election".
The losses came as support has increased for Germany's Green Party as well as the anti-immigrant Alternative for Germany, or AfD.
"This would have been unthinkable in 2013, when she nearly won an outright majority in the Federal elections", he added. But she has been a stalwart face of Western democracy through turbulent times, including the European debt crisis, the migrant influx of 2015, Britain's decision to leave the EU and escalating trade tensions with the United States.
"This may be one reason why Merkel sticks around a bit longer", Campbell said.
The repeated electoral beatings have hurt Merkel and severely damaged the ruling coalition as the SPD blames chancellor's policies for its slump in the ballot box.
Mr Juncker has made clear that he will not run for a second term as President of the European Commission when his current spell expires in November 2019.
Die Welt reporter Robin Alexander had earlier tweeted that said the path could now be clear for Merkel's chosen heir, CDU general secretary Annegret Kramp-Karrenbauer, to take the reins if no other credible candidate emerges by December.
The coalition of the CDU and the Social Democrats (SPD) nearly collapsed, first over disputes on immigration policy, and then over the fate of a domestic intelligence chief.
Merkel's coalition was twice on the brink of collapse, once over immigration policy and then over a dispute about the fate of the domestic intelligence chief who was accused of harbouring far-right views. "The CDU should make way for a new start in a government or a new election in Germany", he told NTV, a TV channel. The party leader in the state, Tarek Al-Wazir, whose parents are Yemeni, said before the vote that anyone who wanted to send a message of rejection to the far-right AfD they "could do no worse than vote for a party led by someone like me".
Often hailed as the world's most powerful woman and Europe's de facto leader, a weakened Merkel has faced growing calls to spell out her succession plans after 13 years in power.