We reported last year that the 24-year-old Dane had negotiated his own 2016 Renault seat, and was also assisted by his billionaire sponsor Anders Holch Povlsen as he put together his new multi-year Haas deal.
Now, Ekstra Bladet newspaper says a court battle with Riis Madsen will begin on June 1.
The case will be heard in Copenhagen, with Magnussen's former manager claiming damages for the driver's current and future income over breach of contract.
"Attempts at an out of court settlement have failed," the Danish newspaper claimed.
Former Danish racing driver Jason Watt said disputes over long-term contracts in motor racing are nothing new.
"Contract lengths of 10-15 years are not unusual," he said. "A manager puts in money to build a career and it may take years before there is a return."
Riis Madsen would not comment, and Magnussen said only: "I have nothing to say at this time."