News agency Dpa said that Horst Seehofer, the leader of the Bavarian-only Christian Social Union which is in coalition with Mrs Merkel, was planning to announce his resignation.
Seehofer and Merkel have been at odds over Germany's approach to mass migration.
If Seehofer does resign, it is unclear whether the CSU would seek to remain in coalition with Merkel's CDU and offer a replacement interior minister.
"Horst Seehofer is not concerned with finding a solution to migration policy; he wants to open the door to right-wing populism and overthrow the chancellor", she said.
Merkel and Seehofer have been embroiled in a row for weeks over the interior minister's plan to start turning away migrants at the German border who have already registered elsewhere in the European Union (EU).
"For the Christian Social Union (CSU) it is of utmost importance not to lose its credibility.The promise has been that Seehofer would stop immigration of those who are not entitled to go through the asylum procedure in Germany".
Mr. Seehofer had already offered his resignation late on Sunday evening during the CSU leadership's meeting. The CDU's leaders, who are now gathered in Berlin for a second straight day of discussions, said they still see room for a compromise solution in the migration dispute.
Leaders said they would consider setting up "disembarkation platforms" outside the European Union, most likely in North Africa, in a bid to discourage migrants and refugees boarding EU-bound smuggler boats.
By letting the CSU tear itself apart over its future in the coalition, Merkel may yet rid herself of a formidable foe in Seehofer - as she has with a string of other top conservatives in her 12-1/2 years in office.
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The quarrel threatens to derail Germany's fragile coalition and the 70-year-old alliance of CDU and CSU.
"We clearly decided we don't want to jeopardise, with unilateral border rejections, what we've achieved in Europe", Elmar Brok, a senior European lawmaker and CDU board member, told DLF public radio on Monday.
"We'll have more talks today with the CDU in Berlin with the hope that we can come to an agreement", Mr Seehofer told reporters just before 2am on Monday. This could see to her trying to lead a minority government, or possibly new elections.
Merkel also secured agreement from Greece and Spain to take back from Germany migrants who previously registered in those countries.
The CSU's hard line on migration comes amid a growth in support for the far-right Alternative for Germany (AfD) party in Bavaria, where state elections will be held in October.
He added that he meant to stay on in his cabinet post after earlier threatening to quit.
Merkel, now barely 100 days into her fourth term, faced a backlash from the conservative CSU after allowing more than one million asylum-seekers into Germany since 2015.
The EU and bilateral deals were "only possible because the chancellor enjoys respect and authority throughout Europe", Germany's EU Commissioner and CDU politician Guenther Oettinger said in an interview with the Frankfurter Allgemeine Sonntagszeitung weekly.
"As a result Italy will be in the position to have really good reasons for no longer accepting any people coming to Italy by the Mediterranean", Patzelt says, adding that this would be exactly the result the CSU intends.
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