Ms Maréchal-Le Pen, 27, who is an MP for the National Front (FN), had been seen by some as a future leader of the party.
She is the granddaughter of FN founder Jean-Marie Le Pen.
She is one of the best known figures in the party and one of only two FN lawmakers in the outgoing parliament.
Analysts say she takes more of a hardline position than her aunt.
According to Le Figaro, Ms Maréchal-Le Pen will announce on Wednesday her intention not to stand for a new term in parliamentary elections in June. She will also quit her position as president of the FN in the south-eastern region of Provence-Alpes-Côte d'Azur.
It is understood she wishes to spend more time with her young daughter, the newspaper adds.
The party would not confirm the report but senior FN official Bruno Gollnisch told reporters it would not be totally unexpected.
"I think it's in the works, but I will let her announce it if she wants to," he said.
Marion Maréchal-Le Pen, the niece of defeated far-right French presidential candidate Marine Le Pen, is to quit politics, French media report.