A spokesperson for the prosecutor said no decision had been taken. "No decision has been made at this stage of the investigation and no timeframe has been agreed as of today," she said.
Mr Fillon told supporters during a visit to the French Indian Ocean island of Reunion that he was determined to stay in the presidential campaign until the end.
"My friends, for a fortnight, I have been attacked 24 hours a day but I will fight until the end because my project is the only one capable of reviving France," he said.
The couple's lawyer did not respond to a request for comments. Mr Fillon has confirmed that his wife was paid but has said the work was genuine.
His lawyers have questioned the legal legitimacy of the case and have asked the financial prosecutor to drop it.
Mr Fillon, who has rallied his party behind him, is fighting to keep his campaign alive and has said he will step down if he is put under formal investigation.
Opinion polls since the scandal broke almost three weeks ago show him slipping out of the race, with voters turned off by the probe into a report by the Canard Enchaine satirical weekly that his wife was paid hundreds of thousands of euros in taxpayers' money for work she may not have done.
The polls, which before the affair saw him as favourite to win the presidency, show the 62-year-old former prime minister coming a close third in the first round vote on April 23. That would leave first- and second-placed Marine Le Pen of the National Front and centrist Emmanuel Macron to contest the May 7 second round, a runoff the polls show Mr Macron winning comfortably.
According to the newspaper, there are two potential routes the prosecutor will take. The first would be to refer the case to an investigating magistrate, whose role is to decide whether a person or people should be put under formal investigation.
Sometimes these referrals can be brought against an unnamed party, but in this case, the newspaper said, it would involve named parties.
The second route would be to put the case directly before a criminal court. Under this scenario, the newspaper said, proceedings could start at the earliest within 11 days.
The JDD also said, however, that the criminal court might decide to call a halt to the proceedings - observing what it called an "electoral truce".
While campaigning for the ticket to represent his party, Mr Fillon emphasised that he had a clean judicial record and that he would cut back on wasteful government spending.
Should The Republicans party need to choose a new candidate, the cut-off date for the collection of signatures is March 17.
The probe into the Fillon family earnings has extended to payments made to two of the couple's children. Mr Fillon's office in parliament has been searched, and all four people have been interviewed by police investigators.
Although financial and personal scandal has brought an end to many a French political career, the Fillon affair is unprecedented in that it surrounds a candidate elected by an open public vote - a first for his party and a relatively new concept in France.