Three candidates have revealed plans to stand for the top party job in December: CDU general secretary Annegret Kramp-Karrenbauer, health minister Jens Spahn and former chief of the party's parliamentary group Friedrich Merz.
Another name touted by German media is Armin Laschet, a Merkel ally who is state premier of Germany's most populous region North Rhine-Westphalia.
But the new leader will raise questions about Angela Merkel's pledge to stay on as chancellor until her mandate ends in 2021.
Spiegel said if Kramp-Karrenbauer (who is nicknamed AKK) wins the race, “then Merkel's chances at staying in power are good”.
If either a Merkel critic like Spahn or Merz gets the top job, “then Merkel's chancellorship will likely be over more quickly”.
Two separate polls by business daily Handelsblatt and Spiegel Online show that 62-year-old Merz is currently the frontrunner.
According to a poll on Spiegel Online published Tuesday, 33.7 percent of more than 5,000 respondents voted for Merz, whereas 19.2 percent opted for Kramp-Karrenbauer, a confidant of the current chancellor who has often been dubbed a mini-Merkel.
The majority of Merz supporters don't hail from the CDU but rather from the Free Democrats (FDP) or Alternative for Germany (AfD). According to the Spiegel Online poll, about half of AfD supporters favoured Merz, whereas about a quarter of FDP supporters would like to to see him as the new CDU leader.
Merz, who announced his candidacy on Tuesday, has nursed a grudge against Merkel for driving him out as head of the CDU's parliamentary group in 2002.
Following his defeat at her hands, he returned to work as a lawyer and heads the supervisory board of mammoth asset manager Blackrock's German arm.
Like Spahn, the financial policy expert and social conservative Merz has complained that Merkel led the CDU too far to the left.
In the poll, Merz also scored highest among those aged over 65 and the lowest among those aged between 18-29. “The question is whether he can win the support of those who never saw him in senior political circles,” the news website wrote.
Merkel has said she would not put her thumb on the scale for any candidate, but “will accept any democratic decision taken by my party”.
Merkel long enjoyed the support of German voters as a guarantor of stability and prosperity.
But her power has been on the wane since her 2015 decision to keep Germany's borders open at the height of Europe's migrant crisis, ultimately allowing in more than one million asylum seekers.
The mass arrivals left a deep rift in German society, and fuelled the rise of the far-right AfD, fundamentally redrawing the political map.
Observers also note that she is no longer the master of Germany's political calendar.
“Whether Merkel will really govern as chancellor until 2021 and then leave politics as promised, or whether the events would suddenly become uncontrollable for her, is no longer up to her alone,” said Spiegel.
Wolfgang Schäuble, Bundestag president and former finance minister, noted that “there are three years to go in the legislature period. We will see if that will really be the case.
She is maybe now no longer as strong as (she was) at the peak of her success,” Schäuble added in an interview with public broadcaster Deutsche Welle.
Besides the CDU internal power struggle that could determine her future, her departure could also be precipitated if a junior coalition partner, the Social Democratic Party, pulls the plug prematurely.
The SPD will review by autumn 2019 “whether this government is still the right place for us”, party chief Andrea Nahles said.