According to La Provence, Marseille have identified the 25-year-old Japanese international as one of their preferred options following the departures of Mason Greenwood, Hamed Junior Traore and Pierre-Emerick Aubameyang.
Nakamura joined Reims from LASK for €12 million in 2023 and has since become an important player for the club.
He made 32 appearances last season, starting 29 matches, while scoring 14 goals and providing three assists. His strong World Cup campaign further enhanced his reputation.
However, Marseille face competition from Everton, Bournemouth and Fulham, while financial constraints could complicate negotiations.
Nakamura has previously expressed a desire to leave Reims, who have granted him permission to depart if the right deal is found.