The current government leaves office in May.
Bruno Le Roux denies he has done anything wrong but says he does not want the scandal to affect the government's work.
Fillon had been a frontrunner in the presidential race until the scandal, relating to the allegedly fictitious employment of his wife, Penelope Fillon, and two children, dented his support.
Further allegations against Fillon have also been published by the same newspaper today.
Earlier, Le Roux admitted that he paid two of his daughters €55,000 of public money over seven years by employing them as his parliamentary assistants during college holidays.
The Quotidien show reported on Monday that Le Roux had employed his two daughters, one when she was in secondary school and one just after leaving school, several times as parliamentary assistants during summer breaks.
Une minute de silence en mémoire des victimes des attentats de Bruxelles
La Belgique multiplie ce mercredi les cérémonies du souvenir, un an après les attentats qui ont fait trente-deux morts et des centaines de blessés à Bruxelles.
Le Canard Enchaîné fait de nouvelles révélations stupéfiantes — François Fillon
Problème, ce dernier avait rejoint le conseil d'administration d'une des sociétés du milliardaire dans les années 1980. Des fonds ont-ils pu être levés, pour financer sa campagne électorale? Sur ce sujet, aucun commentaire n'est fait.
Présidentielle: la Loire avec Jean Lassalle
D'autres étaient plus loin du compte, comme Rama Yade, ancienne ministre du président Nicolas Sarkozy, avec 217 signatures. Dix candidats avaient pu se présenter en 2012, 12 en 2007 et seize - un record sous la Ve République - en 2002.
"The most prudent decision would be for him to choose to resign", he said. The new interior minister was named on Tuesday afternoon as Matthias Fekl.
"No one today can prevent me being a candidate", Fillon said in a TV interview in which he again said an investigation into allegations he gave his wife a highly paid fake parliamentary job was politically motivated. The issue has been brought into sharp focus with the scandal dubbed "Penelopegate" that has hit Fillon's presidential bid.
An Elabe poll of voting intentions, conducted after Monday's televised debate of five leading candidates, showed Macron had slightly increased his lead over Le Pen with 26 percent to her 24.5 percent in the first round.
But the French public is growing frustrated with a political establishment it sees as enriching itself while average workers suffer, and there is growing public pressure for transparency.
Rouban added: "The high rate of unemployment makes the idea that some people can benefit from their position to get rich, even if it's legal, seem even more intolerable".