Ms Kramp-Karrenbauer is aiming to give up leadership of the CDU in the summer.
CDU insiders said she wanted to “organise the process of the chancellor candidacy during summer, prepare the party for the future and then hand over the party chair”.
But the party source revealed Angela Merkel wants Ms Kramp-Karrenbauer to remain as a party minister.
The CDU leader said this morning in a party meeting there was an unresolved relationship between parts of the CDU with the AfD and the Left.
She is strictly against cooperation with these parties.
Ms Kramp-Karrenbauer also claimed it is obvious party presidency and chancellorship or the candidacy for chancellorship belong in one hand.
This marks the latest blow to German politics in what has been a chaotic year for the country.
Ms Kramp-Karrenbauer has been struggling to assert her control over her conservative party after a regional branch defied her by backing a local leader helped into office by the far right.
The controversy occurred in the eastern German state, Thuringia, when Bodo Ramelow, the leader of the state, was toppled by a political collaboration which drew together the far-right AfD and the CDU.
Mr Ramelow’s Die Linke party was victorious in Thuringia’s state elections last year, and the party recently agreed to a coalition deal.
However, in a shock political manoeuvre, Mr Ramelow then lost the vote for state premier as the AfD backed another candidate.
It was widely expected Mr Ramelow would be re-elected with ease to form a minority government in the third round of voting.
Instead, underdog candidate Thomas Kemmerich of the Free Democratic Party clinched a small victory of 45 votes to 44.
Ms Kramp-Karrenbauer said local CDU politicians acted directly “against her will” in backing Mr Kemmerich, and the party chief vowed to push for snap elections to resolve the matter.
It marked the first time the AfD had played a role in forming a government in Germany.
German Chancellor Mrs Merkel branded the election “unforgivable”.
She called the vote a “bad day for democracy” and said it should be reversed.
Speaking during a visit to South Africa shortly after the results were announced, Mrs Merkel condemned the vote by MPs.
The Chancellor said: “It was a bad day for democracy, a day that broke with the long and proud tradition of the CDU’s values.
“This is in no way in line with what the CDU thinks, how we have acted throughout our party’s existence.”
This is a breaking story. More to follow.