The shock revelation comes just as Angela Merkel sets her sights on Martin Schulz's Social Democrat Party to save her from enduring another election.
Mrs Merkel's previous attempt at forming a government collapsed last week when coalition talks failed to reach an agreement.
Stefanie Bolzen, who reports for German paper Die Welt, told the BBC that those inside her own CDU party calling for her to resign were becoming more vocal.
BBC
The people inside her own CDU party calling for her to resign are getting louder She explained that Germany had not faced a political crisis like this for decades and "anything could now happen".
Despite assumptions that Mrs Merkel, who continues to lead the country as interim Chancellor, will eventually form a new government, Bolzen said this was increasingly in doubt.
She told BBC's Dateline programme: "Even if Schulz goes into talks with Merkel, current polling shows a majority of members SPD do not want this, and they will need to vote on this.
"This means even if the elite and leadership want it, another grand coalition is unlikely.
"At the moment, Merkel is watching the other parties collapsing, but she has to be careful because there are voices growing every day in the CDU calling for new leadership."
German election: Photos from the election
Mon, September 25, 2017 
REUTERS
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Demonstrators scuffle with police during the protest against the anti-immigration party Alternative for Deutschland AfD, after German general election (Bundestagswahl) in Berlin
There are growing voices every day in the CDU calling for new leadership
Stefanie Bolzen
This follows remarks earlier today when Chancellor Merkel set out her latest path to forming a stable government.
Merkel’s fourth term was cast into doubt when the pro-business Free Democrats walked out of talks with her conservative bloc and the Greens last Sunday, causing a political crisis in Europe’s biggest economy.
This morning, she told party officials: "Europe needs a strong Germany, it is desirable to get a government in place quickly.
"Asking voters to go to the polls again would, I think, be totally wrong."
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Sunday, 26th November 2017
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