The 26-year-old was a real breakout for Japan at this summer’s World Cup, staring all four of their games, scoring one and providing one assist.
Nakamura ended last season as Reims’ top goal scorer with 14 goals across all competitions and was made Japan’s first choice left-winger after Kaoru Mitoma's was ruled out with a hamstring injury.
According to BBC Sport, newly promoted Hull are looking to sign Nakamura from French side Stade de Reims following their relegation to Ligue 2.
Despite dropping down, Stade de Reims still value the winger at £21.5 million and aren’t under any immediate pressure to sell with Nakamura contracted until 2028.
It is understood, however, that Nakamura is keen on moving to the Premier League having previously been linked with Brighton at Everton.
Spain's Villarreal and Turkish giants Besiktas have already had offers reaching up to £15.5m rejected by his current club.
Hull have had a bust summer as they prepare for life back in the Premier League, adding 11 players including fellow Japan international Hidemasa Morita.