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.

James Purnell said it would increase non-payment and cost the BBC £200m.
The sum is the equivalent of BBC Four, CBBC and CBeebies, which would have to be taken off air, Mr Purnell said at an event to  relaunch the iPlayer service.
Culture Secretary Maria Miller said the move should be discussed during talks to renew the BBC's charter before 2017.
Mr Purnell, who previously held the post in the Labour government, said "it would be a huge risk to do it now".
"The choice would be: either we take those services off or the government would have to have a higher licence fee," he said in reference to BBC Four - the arts and culture channel - and the BBC's children's stations.
He argued decriminalisation would inevitably lead to greater non-payment of the TV licence, which would force an increase in the fee.
It is currently £145.50 and has been frozen at that annual amount since 2010. It is needed to watch or record live broadcasts on any device.
In 2012 about 155,000 people were convicted and fined for not paying the licence fee, while there were some 180,000 prosecutions.
Mr Purnell added downgrading licence fee evasion to a civil offence would penalise the poor.
"Either you have a low penalty - in which case the evasion rates would go up and everyone would have to pay a higher licence fee - or a penalty which is higher and more difficult to pay," he said.
The BBC has previously said "legislation is a matter for the government".
"Just a 1% increase in evasion would lead to the loss of around £35m, the equivalent of around 10 BBC local radio stations," it added.
The government has floated the idea to ease pressure on the courts system.
But it will not be discussed before charter renewal talks - which determine how the BBC is funded what it does and how it is managed.
The current BBC charter runs out in 2016.
Meanwhile, Labour MP John McDonnell has tabled an Early Day Motion in parliament calling on the BBC to reverse its decision to close BBC Three as a television channel.
The motion stated BBC Three has been the home of programmes including Gavin and Stacey, and raised fears changes could lead to compulsory redundancies.
It added the BBC should receive a licence fee increase that tracks inflation when the corporation's charter is renewed next year.
The centre-right candidate for the French presidency, Francois Fillon, is set to tackle allegations of improper payments made to family members.
[NEXT_CONCEPT]
Decriminalising TV licence fee evasion could close BBC channels, the corporation's strategy director has warned.