Linda Evangelista is asking for $46,000 in child support from the father of her son Augustin James.
Papers filed in a New York court by the cover girl earlier this summer named Francois-Henri Pinault – one of the richest men in France – as the father of her only child.
His company PPR has shares in luxury brands such as Gucci, Stella McCartney and Alexander McQueen.
Her lawyers have argued that, as a single mother, she needs the financial support to pay for nannies and chauffeurs to assist with four-year-old, the New York Post reports.
"That would probably be the largest support order in the history of the family court," support magistrate Matthew Troy commented.
Asked about her need for 24-hour childcare, Linda replied that she sometimes works 16-hour days.
She added: "On days when I do not work, I am working on my image; I have to hit the gym. I have beauty appointments.
"I have to work toward my next job and maintaining my image, just like an athlete."
The French billionaire has two other children from a previous marriage, which ended in divorce in 2004.
He also has a daughter, Valentina – who will be four in September – with his wife actress Salma Hayek.
The couple married in 2009.