The incumbent prime minister of France, Jean Castex, assumed office in 2020 after the resignation of his predecessor Edouard Philippe and his cabinet ahead of a government reshuffle.
"Emmanuel Macron would certainly like to appoint a woman to the Matignon [residence of the French prime minister]. But we should not reduce the whole political situation to the prime minister candidacy," Beaune told French broadcaster BFMTV.
Among the candidates considered for the post is Labour Minister Elisabeth Borne, according to the report.
The French presidential runoff was held this past Sunday. The interior ministry has confirmed Macron as the victor with 58.54% of the vote, against 41.46% of his right-wing rival Marine Le Pen.