He will address supporters from his campaign headquarters, in what an aide described as a fight-back.
Mr Fillon's bid has been overshadowed by claims, which he denies, that his wife and two of his children were paid for non-existent parliamentary work.
Some in his party, The Republicans, feel he should drop out of the race.
Recent polls have suggested that he may be eliminated in the first round of the presidential election in April, paving the pay for a possible run-off between centrist Emmanuel Macron and far-right leader Marine Le Pen.
Fillon payment inquiry: What you need to know
But a source close to Mr Fillon told AFP news agency that the candidate "will not give up". The conservative Figaro newspaper said that Monday's speech would mark the start of a "counter-offensive".
Mr Fillon, a 62-year-old former prime minister, has denied wrongdoing and strongly defended his wife, Penelope.
Last month Le Canard Enchaine newspaper reported that she earned 500,000 euros ($534,000; Â£428,000) as her husband's parliamentary assistant between 1998 and 2012, and questioned how much work she had done.
The paper also said Mrs Fillon was paid 100,000 euros for little apparent work at a literary review owned by a billionaire friend of the family - an allegation that could lead to corruption charges against her husband.
It subsequently emerged that Mr Fillon had hired two of his children to act as lawyers, paying them 84,000 euros between 2005 and 2007 - when they were students.
Investigators have begun an inquiry into the reports. Mr Fillon said he would step down if placed under formal investigation.
Until the reports emerged, Mr Fillon was the front-runner for the presidential election, thanks in part to his image as a forthright, honest politician.
The practising Catholic enjoyed a landslide victory over Alain Juppe, another former prime minister, in a party primary in November.
The centre-right candidate for the French presidency, Francois Fillon, is set to tackle allegations of improper payments made to family members.