Andreas Ritzenhoff, the owner of an aluminium manufacturing company, told the Funke newspaper group the chancellor's Christian Democratic Union (CDU) needs a “change of direction” and “new political aims”.
“I'm worried about what's happening with Germany, Europe and the western world,” he said.
“I see here a threat that is directed against the economic power, the prosperity, the security and last but not least the freedom of culture and the spirit of our population.”
Ms Merkel, Germany's leader since 2005 and CDU leader since 2000, has indicated she is likely to seek a new two-year term at the party's helm at a congress in December.
Her authority has been weakened recently by constant squabbling in her fourth-term government and the ousting last week of a close ally as the conservatives' parliamentary leader.
In July, Ms Merkel faced one of the biggest crises of her time in office when the interior minister, Horst Seehofer, tendered his resignation over her migration policy.
However, the chancellor was able to strike a deal with Mr Seehofer, leader of coalition partner the Christian Social Union, preventing the collapse of her government.
Alongside Mr Ritzenhoff, law student Jan-Philipp Knoop has said he plans to challenge Ms Merkel.
Additional reporting by AP
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