The parliament accuses Le Pen's anti-EU National Front (FN) of using funds meant for parliamentary assistants to pay staff for party work in France between 2012 and 2017.
The allegations, which Le Pen denies, have triggered an investigation in France.
The parliament had initially estimated the amount of the contested salaries at 1.9 million euros but now believes the FN wrongfully expensed 4,978,122 euros, the source said, quoting a note to French investigators from the parliament's legal team.
Patrick Maisonneuve, a lawyer for the parliament, confirmed the amount to AFP.
The parliament believes 17 FN lawmakers in the European Parliament, including Le Pen, used European money to pay assistants for work outside the assembly, the source said.
French investigators have not said how many of the jobs are in question.
Le Pen, who came second in the first round of the presidential election behind centrist Emmanuel Macron, has portrayed the allegations as part of a plot to stymie her political ambitions.
She will go up against Macron in a run-off vote on May 7.
In March, Le Pen invoked her MEP's immunity in refusing to submit to questioning by investigating magistrates.
Her chief of staff Catherine Griset and another party official have been charged with concealment.
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