Le Figaro quotes party founder Le Pen as telling its weekly magazine that he wants his granddaughter to assume his candidacy instead.
A top party official, Florian Philippot, said on i-Tele television that Le Pen had discussed the decision with party leadership.
Le Pen’s daughter Marine has led the anti-immigrant party to electoral successes in recent years and sought to clean up its racist image.
Last week she said she opposed her 86-year-old father’s candidacy in the regional elections, and wanted him disciplined for anti-Semitic and other offensive remarks.
Mr Le Pen said in a statement on his Twitter account that the outcry within the party over his remarks “risks dangerously weakening our movement”.
“I will not be complicit with this manoeuvre,” he said.
By standing down, Mr Le Pen avoids possible formal exclusion as a candidate on Friday, when the National Front’s political bureau meets to designate who will run in the December election.
Marine Le Pen says she has decided to send her father before a party disciplinary board for repeating that the Nazi gas chambers were a “detail” in the history of the Second World War - a remark for which he has been convicted - and for voicing support for Philippe Petain, who headed France’s collaborationist Vichy government during the war.
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